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venn diagram
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. What is the meaning of complement in set theory?
A.
B.
C.
D.
____
2. What is the meaning of disjoint in set theory?
A.
B.
C.
D.
____
The English language and the French language are disjoint sets.
Hockey equipment and lacrosse equipment are disjoint sets.
Band instruments and orchestral instruments are disjoint sets.
Linear equations and quadratic equations are disjoint sets.
6. Which pair of sets represents disjoint sets?
A.
B.
C.
D.
____
Trigonometry is a subset of mathematics.
The cities in Manitoba are a subset of the cities in Canada.
Squashes are a subset of vegetables.
Birds are a subset of mammals.
5. Which statement is true?
A.
B.
C.
D.
____
a set with an infinite number of elements
a set of all the elements under consideration for a particular context
a set with a countable number of elements
a set that contains every possible element
4. Which statement is false?
A.
B.
C.
D.
____
two or more sets having no elements in common
two or more sets that do not match
sets that are in different universal sets
sets that contain no elements
3. What is the universal set?
A.
B.
C.
D.
____
all the elements in the universal set that are not identical
a set of elements that work well with a given set
all the elements of a universal set that do not belong to a subset of it
all the elements that are the opposite of the elements in a given set
N, the set of natural numbers, and I, the set of integers
T, the set of all triangles, and C, the set of all circles
N, the set of natural numbers, and P, the set of positive integers
none of the above
7. Which pair of sets represents equal sets?
A.
B.
C.
D.
____
8. Which pair of sets represents one set being a subset of another but is not equal?
A.
B.
C.
D.
____
N, the set of natural numbers, and I, the set of integers
T, the set of all triangles, and C, the set of all circles
N, the set of natural numbers, and P, the set of positive integers
none of the above
N, the set of natural numbers, and I, the set of integers
T, the set of all triangles, and C, the set of all circles
N, the set of natural numbers, and P, the set of positive integers
none of the above
9. Rahim described the set as follows:
• M = {all of the foods he eats}
• D = {his favourite desserts}
• V = {his favourite vegetables}
• F = {his favourite fruits}
Which are the disjoint sets?
A.
B.
C.
D.
____
M and D
M and V
M and F
V and F
10. Rahim described the set as follows:
• M = {all of the foods he eats}
• D = {his favourite desserts}
• V = {his favourite vegetables}
• F = {his favourite fruits}
Assume Rahim likes some fruit for dessert. Which statement is true?
A.
B.
C.
D.
____
The universal set is D, Rahim’s favourite desserts.
Set F is a subset of D.
Set D is a subset of V.
Set M and set V are mutually exclusive.
11. Which Venn diagram correctly represents the situation described?
Rahim described the set as follows:
• M = {all of the foods he eats}
• D = {his favourite desserts}
• V = {his favourite vegetables}
• F = {his favourite fruits}
Assume Rahim likes some fruit for dessert.
A.
B.
C.
D.
____
12. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which set represents the odd, prime numbers of set U?
A.
B.
C.
D.
____
{0, 3, 5, 7, 11, 13, 17, 19}
{3, 5, 7, 11, 13, 17, 19}
{2, 3, 5, 7, 11, 13, 17, 19}
{1, 2, 3, 5, 7, 11, 13, 17, 19}
13. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which is the complement of P?
A.
B.
C.
D.
____
the even numbers of U
the universal set excluding the set of X
the positive integers greater than 20
the non-prime numbers of U
14. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which diagram represents the situation?
A.
B.
C.
D.
____
15. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Which statement describes O?
A.
B.
C.
D.
____
the set of even numbers of U
the set of odd numbers of U
the set of odd, prime numbers of U
the set of even, prime numbers of U
16. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student council are
shown in the Venn diagram. Use the diagram to answer the following questions.
How many students are in both the yearbook club and on the student council?
A.
B.
C.
D.
____
2
5
1
7
17. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student council are
shown in the Venn diagram. Use the diagram to answer the following questions.
How many students are in the yearbook club but not on student council?
A.
B.
C.
D.
____
2
5
1
7
18. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student council are
shown in the Venn diagram. Use the diagram to answer the following questions.
How many students are in at least one of the yearbook club or on student council?
A.
B.
C.
D.
____
2
5
8
7
19. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student council are
shown in the Venn diagram. Use the diagram to answer the following questions.
How many students are on the student council but not in the yearbook club?
A.
B.
C.
D.
____
2
5
1
7
20. There are 28 students in Mr. Connelly’s Grade 12 mathematics class.
The number of students in the yearbook club and the number of students on student council are
shown in the Venn diagram. Use the diagram to answer the following questions.
How many students are neither in the yearbook club nor on student council?
A.
B.
C.
D.
____
2
5
1
20
21. Consider the following Venn diagram of herbivores and carnivores:
Determine H  C.
A.
B.
C.
D.
____
{moose, rabbit, deer, squirrel}
{bear, raccoon, badger}
{cougar, wolf}
{moose, rabbit, deer, squirrel, bear, raccoon, badger, cougar, wolf}
22. Consider the following Venn diagram of herbivores and carnivores:
Determine n(H  C).
A.
B.
C.
D.
____
2
9
4
3
23. Consider the following Venn diagram of herbivores and carnivores:
Determine H  C.
A.
B.
C.
D.
____
{moose, rabbit, deer, squirrel}
{bear, raccoon, badger}
{cougar, wolf}
{moose, rabbit, deer, squirrel, bear, raccoon, badger, cougar, wolf}
24. Consider the following Venn diagram of herbivores and carnivores:
Determine n(H  C).
A. 2
B. 9
C. 4
D. 3
____
25. Consider the following Venn diagram of foods we eat raw or cooked:
Determine H  C.
A.
B.
C.
D.
____
{fish, spinach, apples, cucumber, lettuce, chicken, pork, rice, pasta, potatoes}
{chicken, pork, rice, pasta, potatoes}
{cucumber, lettuce}
{fish, spinach, apples}
26. Consider the following Venn diagram of foods we eat raw or cooked:
Determine H  C.
A.
B.
C.
D.
____
{fish, spinach, apples, cucumber, lettuce, chicken, pork, rice, pasta, potatoes}
{chicken, pork, rice, pasta, potatoes}
{cucumber, lettuce}
{fish, spinach, apples}
27. Consider the following Venn diagram of foods we eat raw or cooked:
Determine n(H  C).
A.
B.
C.
D.
____
2
5
10
3
28. Consider the following Venn diagram of foods we eat raw or cooked:
Determine n(H  C).
A.
B.
C.
D.
____
2
5
11
3
29. Consider the following two sets:
• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Which Venn diagram correctly represents these two sets?
A.
B.
C.
D.
____
30. Consider the following two sets:
• C = {–10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Determine n(C  B).
A.
B.
C.
D.
____
31. Consider the following two sets:
• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Determine n(A  B).
A.
B.
C.
D.
____
3
8
11
19
8
11
16
20
32. Consider the following two sets:
• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Determine A  B.
A.
B.
C.
D.
____
33. Consider the following two sets:
• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Determine A  B.
A.
B.
C.
D.
____
{3, 6, 9, 12}
{–6, 0, 6}
{0}
{–6, 0, 6, 12}
35. Consider the following two sets:
• C = {–10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Determine C  B.
A.
B.
C.
D.
____
{3, 6, 9, 12}
{0, 3, 6, 9, 12}
{1, 2, 4, 5, 7, 8, 10, 11}
{–9, –6, 6, 9}
34. Consider the following two sets:
• C = {–10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10}
• B = {–9, –6, –3, 0, 3, 6, 9, 12}
Determine C  B.
A.
B.
C.
D.
____
{–9, –6, –3, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12}
{0, 1, 2, –3, 4, 5, –6, 7, 8, –9, 10, 11, 12}
{1, 2, 4, 5, 7, 8, 10, 11}
{–9, –6, –3, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
{–10, –9, –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
{–10, –9, –8, –6, –4, –3, –2, 0, 2, 3, 4, 6, 7, 9, 10}
{–10, –9, –8, –6, –4, –3, –2, 0, 2, 3, 4, 6, 7, 9, 10, 12}
{–10, –9, –7, –6, –4, –3, –2, 0, 2, 3, 4, 6, 7, 9, 10, 12}
36. The three circles in the Venn diagram (P, Q, and R ) contain the same number of elements. Which
set of values is true for p, q, and r?
A.
B.
C.
D.
____
p = 11, q = 11, r = 5
p = 7, q = 8, r = 2
p = 7, q = 6, r = 1
p = 14, q = 13, r = 7
37. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows
the types of activities the campers like.
Use the diagram to determine n((R  C) \ A).
A.
B.
C.
D.
____
64
48
37
59
38. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows
the types of activities the campers like.
Use the diagram to determine n((R  A) \ C).
A. 14
B. 5
C. 26
D. 8
____
39. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows
the types of activities the campers like.
Use the diagram to determine n((A  C)  (R  A)).
A.
B.
C.
D.
____
16
27
5
11
40. A summer camp offers canoeing, rock climbing, and archery. The following Venn diagram shows
the types of activities the campers like.
Use the diagram to determine n((A \ C) \ R).
A.
B.
C.
D.
____
8
22
6
5
41. A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the types
of food the customers like.
Use the diagram to determine n(K \ T).
A.
B.
C.
D.
____
10
19
50
23
42. A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the types
of food the customers like.
Use the diagram to determine n(C  T).
A.
B.
C.
D.
____
53
15
40
83
43. A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the types
of food the customers like.
Use the diagram to determine n((T  K)  C).
A.
B.
C.
D.
____
71
47
55
93
44. A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the types
of food the customers like.
Use the diagram to determine n(K) – n(C  T  K).
A.
B.
C.
D.
____
10
50
27
33
45. A restaurant offers Chinese, Thai, and Korean food. The following Venn diagram shows the types
of food the customers like.
Use the diagram to determine n(C) – n(T).
A.
B.
C.
D.
____
5
4
10
15
46. Some table games use a board, dice, or cards, or a combination these. The following Venn diagram
shows the number of games that use these tools.
Use the diagram to determine n(U).
A.
B.
C.
D.
____
100
104
97
88
47. Some table games use a board, dice, or cards, or a combination these. The following Venn diagram
shows the number of games that use these tools.
Use the diagram to determine n(C) – n(C  B).
A.
B.
C.
D.
____
39
51
25
28
48. Some table games use a board, dice, or cards, or a combination these. The following Venn diagram
shows the number of games that use these tools.
Use the diagram to determine the number of games that use exactly two of these tools.
A.
B.
C.
D.
____
13
51
25
74
49. Some table games use a board, dice, or cards, or a combination these. The following Venn diagram
shows the number of games that use these tools.
Use the diagram to determine n(B \ D).
A.
B.
C.
D.
____
44
33
67
71
50. Some table games use a board, dice, or cards, or a combination these. The following Venn diagram
shows the number of games that use these tools.
Use the diagram to determine n(D  B).
A.
B.
C.
D.
____
29
25
69
75
51. What is a hypothesis?
A. an idea
B. a statement
C. a clue
D. an assumption
____
52. What is a conclusion?
A.
B.
C.
D.
____
53. What is a converse?
A.
B.
C.
D.
____
If you fall down, get right back up.
Juggling is not hard if you practice.
If the temperature is below freezing, it must be winter.
If the sky is cloudy, then you cannot see the sun.
57. Which sentence is the converse to the conditional statement below?
“If the milk is not refrigerated, then it will spoil.”
A.
B.
C.
D.
____
You can fool some of the people some of the time but you can’t fool me.
If you are a farmer, then you live in the country.
If you can’t beat them, join them.
You get wet if you stand in the rain.
56. Which sentence is written as a conditional statement?
A.
B.
C.
D.
____
a conditional statement that is only true in two cases
a statement that uses the form “if p, then q”
a conditional statement whose converse is also true
a conditional statement whose inverse is also true
55. Which sentence is written as a conditional statement?
A.
B.
C.
D.
____
proof that a conditional statement is false
a conditional statement in which the hypothesis and the conclusion are switched
the second part of a conditional statement
the opposite of a conditional statement
54. What is a biconditional statement?
A.
B.
C.
D.
____
the result of a hypothesis
an assumption
a decision
the answer to a statement
Unrefrigerated milk will spoil.
The milk is spoiled because it was not put in the refrigerator.
If the milk is spoiled, then it is not refrigerated.
The milk will spoil if it is not put in the refrigerator.
58. Which sentence is the converse to the conditional statement below?
“If students are in school, then it is a weekday.”
A. If it is a weekday, then students are in school.
B. If it is not a weekday, then students are not in school.
C. During the week, students are in school.
D. Students go to school on weekdays.
____
59. Which truth tables apply to the conditional statement below and its converse?
“If the milk is not refrigerated, then it will spoil.”
A.
C.
p
q
p
q
pq
pq
T
T
T
T
T
T
q
p
q
p
qp
qp
T
T
T
T
F
F
B.
p
F
q
F
A.
B.
C.
D.
____
q
F
p
F
pq
T
qp
T
q
F
p
F
pq
F
qp
F
A.
B.
C.
D.
60. Which truth tables apply to the conditional statement below and its converse?
“If x = y, then y = x.”
A.
C.
p
q
p
q
pq
pq
T
F
F
T
T
F
q
p
q
p
qp
qp
F
F
F
T
F
T
B.
p
T
q
T
A.
B.
C.
D.
____
D.
p
T
q
T
q
T
p
T
pq
T
qp
T
D.
p
T
q
T
q
F
p
F
A.
B.
C.
D.
61. Which conditional statement is biconditional?
A. If today is Labour Day, then it is November 3.
B. If it is October, then students are in school.
pq
T
qp
F
C. If today is Friday, then tomorrow is Saturday.
D. If there is deep snow outside, then the outside temperature is below freezing.
____
62. Which conditional statement is false?
A.
B.
C.
D.
____
63. Which conditional statement is biconditional?
A.
B.
C.
D.
____
If you live in PEI, then you live in the smallest province.
If you bought a condominium, then you own your home.
If you live in Kelowna, then you live in British Columbia.
If you live in a house, then you have a backyard.
65. Which conditional statement is false?
A.
B.
C.
D.
____
If you live in PEI, then you live in the smallest province.
If you bought a condominium, then you own your home.
If you live in Kelowna, then you live in British Columbia.
If you live in a house, then you have a backyard.
64. Which conditional statement is false?
A.
B.
C.
D.
____
If today is Labour Day, then it is November 3.
If it is October, then students are in school.
If today is Friday, then tomorrow is Saturday.
If there is deep snow outside, then the outside temperature is below freezing.
12 o’clock is midnight if and only if it is not noon.
It is real maple syrup if and only if the syrup is made from maple sap.
It is Valentine’s Day if and only if it is February 14.
It is a whale if and only if is it a mammal that lives in the ocean.
66. What is the inverse?
A. a conditional statement in which the hypothesis and the conclusion are switched
B. a statement that is formed by negating both the hypothesis and the conclusion of a
conditional statement
C. a statement that is formed by negating both the hypothesis and the conclusion of
the converse of a conditional statement
D. a statement that is formed by inverting both the hypothesis and the conclusion of a
conditional statement
____
67. What is a contrapositive statement?
A. a conditional statement in which the hypothesis and the conclusion are switched
B. a statement that is formed by negating both the hypothesis and the conclusion of a
conditional statement
C. a statement that is formed by negating both the hypothesis and the conclusion of
the converse of a conditional statement
D. a statement that is formed by inverting both the hypothesis and the conclusion of a
conditional statement
____
68. Which statement is true?
A. If a conditional statement is true, then its contrapositive is true, and vice versa.
B. If a conditional statement is true, then its converse is true, and vice versa.
C. If the inverse of a conditional statement is true, then the contrapositive of the
statement is also true, and vice versa.
D. If the contrapositive of a conditional statement is true, then the converse of the
statement is also true, and vice versa.
____
69. Which statement is true?
A. If the converse of a conditional statement is true, then the contrapositive of the
statement is also true, and vice versa.
B. If the inverse of a conditional statement is true, then the converse of the statement
is also true, and vice versa.
C. If a conditional statement is true, then its inverse is true, and vice versa.
D. If a conditional statement is true, then its converse is true, and vice versa.
____
70. Which statement is the converse of the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
A.
B.
C.
D.
____
71. Which statement is the inverse of the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
A.
B.
C.
D.
____
If tomorrow is Sunday, then today is not Monday.
If today is Sunday, then tomorrow is Monday.
If tomorrow is not Monday, then today is not Sunday.
If today is not Sunday, then tomorrow is not Monday.
72. Which statement is the contrapositive of the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
A.
B.
C.
D.
____
If tomorrow is Sunday, then today is not Monday.
If today is Sunday, then tomorrow is Monday.
If tomorrow is not Monday, then today is not Sunday.
If today is not Sunday, then tomorrow is not Monday.
If tomorrow is Sunday, then today is not Monday.
If today is Sunday, then tomorrow is Monday.
If tomorrow is not Monday, then today is not Sunday.
If today is not Sunday, then tomorrow is not Monday.
73. What is true about the conditional statement below?
“If tomorrow is Monday, then today is Sunday.”
A.
B.
C.
D.
____
74. Which statement is the converse of the conditional statement below?
“If a bird has wings, then the bird can fly.”
A.
B.
C.
D.
____
The converse and inverse are true but the statement and contrapositive are false.
The statement and contrapositive are true but the inverse and converse are false.
The statement, converse, inverse, and contrapositive are all true.
The statement and inverse are true but the converse and contrapositive are false.
78. Which statement is the inverse of the conditional statement below?
“If a balloon is filled with helium, then the balloon will float upwards.”
A.
B.
C.
D.
____
If a bird does not have wings, then the bird cannot fly.
If the bird cannot fly, then the bird does not have wings.
If a bird can fly, then the bird has wings.
If a bird does not have wings, then the bird can fly.
77. What is true about the conditional statement below?
“If a bird has wings, then the bird can fly.”
A.
B.
C.
D.
____
If a bird does not have wings, then the bird cannot fly.
If the bird cannot fly, then the bird does not have wings.
If a bird can fly, then the bird has wings.
If a bird does not have wings, then the bird can fly.
76. Which statement is the contrapositive of the conditional statement below?
“If a bird has wings, then the bird can fly.”
A.
B.
C.
D.
____
If a bird does not have wings, then the bird cannot fly.
If the bird cannot fly, then the bird does not have wings.
If a bird can fly, then the bird has wings.
If a bird does not have wings, then the bird can fly.
75. Which statement is the inverse of the conditional statement below?
“If a bird has wings, then the bird can fly.”
A.
B.
C.
D.
____
The statement and contrapositive are true but the inverse and converse are false.
The inverse and contrapositive are true but the statement and converse are false.
The converse and inverse are true but statement and contrapositive are false.
The statement, converse, inverse, and contrapositive are all true.
If a balloon floats upwards, then the balloon is filled with helium.
If a balloon is not filled with helium, then the balloon will not float upwards.
If a balloon is not filled with helium, then the balloon will float downwards.
If a balloon does not float upwards, then the balloon is not filled with helium.
79. Which statement is the contrapositive of the conditional statement below?
“If a balloon is filled with helium, then the balloon will float upwards.”
A.
B.
C.
D.
____
If a balloon floats upwards, then the balloon is filled with helium.
If a balloon is not filled with helium, then the balloon will not float upwards.
If a balloon is not filled with helium, then the balloon will float downwards.
If a balloon does not float upwards, then the balloon is not filled with helium.
80. What is true about the conditional statement below?
“If a balloon is filled with helium, then the balloon will float upwards.”
A.
B.
C.
D.
The statement, converse, inverse and contrapositive are all true.
The statement and inverse are true but the converse and contrapositive are false.
The statement and contrapositive are true but the inverse and converse are false.
The inverse and contrapositive are true but the statement and converse are false.
Short Answer
1. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is n(L)?
2. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is n(G)?
3. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is n(F)?
4. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
What is the number of sums less than or greater than 4?
5. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
Describes the relationship between the sets L and G.
6. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
List the subsets using set notation.
7. Tania recorded the 16 possible sums that can occur when you roll two four-sided dice.
• S = {all possible sums}
• L = {all sums less than 4}
• G = {all sums greater than 4}
• F = {all sums equal to 4}
Describes the relationship between events L and G.
8. What is the set notation for the set of all natural numbers greater than 1 and less than or equal to
50?
9. What is the set notation for the set of all positive real numbers that are less than 22?
10. What is the set notation for the set of all integers from –21 to –4 that are a multiple of 2?
11. Draw a Venn diagram to represent these sets.
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
12. Consider the following information.
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
List the subsets using set notation.
13. Consider the following information.
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
List the pairs of disjoint sets.
14. Consider the following information.
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
What is the complement to set S?
15. Consider the following information.
• the universal set U = {all grade 12 courses}
• S = {all social studies courses}
• H = {all history courses}
• G = {all geography courses}
• M = {all mathematics courses}
What new set could belong to set U but not to set S or set M?
16. Carlos surveyed 50 students about their favourite subjects in school. He recorded his results.
Favourite Subject
Number of Students
mathematics
18
science
15
neither mathematics nor science
20
Determine how many students like mathematics and science.
17. Carlos surveyed 50 students about their favourite subjects in school. He recorded his results.
Favourite Subject
Number of Students
mathematics
18
science
15
neither mathematics nor science
20
Determine how many students like only mathematics or only science.
18. Mrs. Lam’s physics class is visiting the local amusement park. She has 32 students. Of these
students, 20 plan to ride the roller coaster and 15 plan to ride the vertical drop. There are 8 students
who do not plan to ride either attraction.
Determine how many students plan to ride both the roller coaster and the vertical drop.
19. Mr. McSherry’s physics class is visiting the local amusement park. He has 33 students. Of these
students, 21 plan to ride the roller coaster and 12 plan to ride the vertical drop. There are 7 students
who do not plan to ride either attraction.
Determine how many students plan to ride only the roller coaster.
20. Given the following situation:
• the universal set U = {positive integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of U}
• O = {odd numbers of U}
Determine n(X and P).
21. If you draw a card at random from a standard deck of cards, you will draw a card that is either red
(R) or black (B). The card will also either be a number card (N) or a face card (F). Determine n(R
 F).
22. If you draw a card at random from a standard deck of cards, you will draw a card that is either red
(R) or black (B). The card will also either be a number card (N) or a face card (F). Determine n(B
 N).
23. If you draw a card at random from a standard deck of cards, you will draw a card that is either red
(R) or black (B). The card will also either be a number card (N) or a face card (F). Determine n(R
 B).
24. If you draw a card at random from a standard deck of cards, you will draw a card that is either red
(R) or black (B). The card will also either be a number card (N) or a face card (F). Determine n(F
 N).
25. If you draw a card at random from a standard deck of cards, you will draw a card that is either red
(R) or black (B). The card will also either be a number card (N) or a face card (F). Determine n(F).
26. A music school offers lessons on 12 different instruments.
piano
bagpipe
guitar
recorder
accordion
clarinet
violin
flute
xylophone
trumpet
steel drum
banjo
Determine the number of instruments with both keys (K) and strings (S).
27. A music school offers lessons on 8 different instruments.
piano
bagpipe
recorder
harmonica
violin
xylophone
steel drum
banjo
Determine the number of instruments with neither keys nor strings, (K  S)´.
28. A music school offers lessons on 8 different instruments.
piano
bagpipe
recorder
harmonica
violin
steel drum
xylophone
banjo
Determine the number of instruments with either more than 6 letters in their name or end in a
vowel (L  V).
29. A music school offers lessons on 12 different instruments.
piano
bagpipe
guitar
recorder
accordion
clarinet
violin
flute
xylophone
trumpet
steel drum
banjo
Determine the number of instruments that are played with sticks or have a mouthpiece (P  M).
30. A music school offers lessons on 12 different instruments.
piano
bagpipe
guitar
recorder
accordion
clarinet
violin
flute
xylophone
trumpet
steel drum
banjo
Determine the number of instruments with strings (S), and with strings and a bow (S  B).
31. A music school offers lessons on 8 different instruments.
piano
bagpipe
recorder
harmonica
violin
xylophone
steel drum
banjo
Determine the number of instruments that have neither a mouthpiece nor keys (M  K)´.
32. Games that use a board include chess, Clue, checkers, Go, Scrabble, and Monopoly. Games that
use cards include Hearts, Monopoly, Snap, and Clue. Draw a Venn diagram to represent these two
sets of games.
33. Games that use a board include chess, Clue, checkers, Go, Scrabble, and Monopoly. Games that
use cards include Hearts, Monopoly, Snap, and Clue. Determine the union and intersection of these
two sets.
34. Flightless birds include the ostrich, emu, penguin, and kiwi. Arctic birds include the snow goose,
Arctic tern, osprey, penguin, and red-tailed hawk. Draw a Venn diagram to represent these two sets
of birds.
35. Flightless birds include the ostrich, emu, penguin, and kiwi. Arctic birds include the snow goose,
Arctic tern, osprey, penguin, and red-tailed hawk. Determine the union and intersection of these
two sets.
36. Grade 12 students were surveyed about their extra curricular activities.
• 58% belonged to a sports team (S)
• 63% belonged to a band or choir (B)
• 47% belonged to a school club (C)
• 24% belonged to a sports team and a band or choir
• 21% belonged to a sports team and a school club
• 36% belonged to a band or choir and a school club
• 19% engaged in all three activities
What percent of students only belong to a band or choir? Write your answer in set notation.
37. Grade 12 students were surveyed about their extra curricular activities.
• 58% belonged to a sports team (S)
• 63% belonged to a band or choir (B)
• 47% belonged to a school club (C)
• 24% belonged to a sports team and a band or choir
• 21% belonged to a sports team and a school club
• 36% belonged to a band or choir and a school club
• 19% engaged in all three activities
What percent of students belong to a sports team or a school club but not a band or choir? Write
your answer in set notation.
38. Grade 12 students were surveyed about their extra curricular activities.
• 58% belonged to a sports team (S)
• 63% belonged to a band or choir (B)
• 47% belonged to a school club (C)
• 24% belonged to a sports team and a band or choir
• 21% belonged to a sports team and a school club
• 36% belonged to a band or choir and a school club
• 19% engaged in all three activities
What percent of students belong to both a sports team and a band or choir but not a school club?
Write your answer in set notation.
39. Grade 12 students were surveyed about their extra curricular activities.
• 58% belonged to a sports team (S)
• 63% belonged to a band or choir (B)
• 47% belonged to a school club (C)
• 24% belonged to a sports team and a band or choir
• 21% belonged to a sports team and a school club
• 36% belonged to a band or choir and a school club
• 19% engaged in all three activities
What percent of students are involved in only one of these activities? Write your answer in set
notation.
40. Grade 12 students were surveyed about their extra curricular activities.
• 58% belonged to a sports team (S)
• 63% belonged to a band or choir (B)
• 47% belonged to a school club (C)
• 24% belonged to a sports team and a band or choir
• 21% belonged to a sports team and a school club
• 36% belonged to a band or choir and a school club
• 19% engaged in all three activities
What percent of students are involved in only two of these activities? Write your answer in set
notation.
41. These nine attribute cards have three different shapes, numbers, and shadings (clear, striped, or
solid). Determine four sets, with three cards in each set. Each set of three cards must have
• the same number or three different numbers, and
• the same shape or three different shapes, and
• the same shading or three different shadings.
All the cards can be used more than once.
42. A men’s magazine surveyed 600 readers about their facial hair.
• 85 had a moustache
• 49 had a beard
• 483 were clean shaven
How many men had a beard and a moustache? Write your answer in set notation.
43. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people travel to work some other way? Use a Venn diagram to show your answer.
44. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people use public transit only? Use a Venn diagram to show your answer.
45. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people use two modes of transportation? Use a Venn diagram to show your answer.
46. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people did not cycle or use public transit? Write your answer using set notation.
47. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people drove or used public transit but did not cycle? Write your answer using set
notation.
48. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people used only one mode of transport? Write your answer using set notation.
49. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people only cycle? Write your answer using set notation.
50. The city surveyed 3000 people about how they travel to work.
• 1978 took public transit (P)
• 1494 drove (D)
• 818 cycled (C)
• 731 took public transit and drove only
• 298 took public transit and cycled only
• 27 drove and cycled only
• 164 used all three modes of transportation
How many people cycle but do not drive? Write your answer using set notation.
51. Write the converse of the conditional statement below.
“If you have insomnia, then you cannot sleep at night.”
52. Write the converse of the conditional statement below.
“If you work in a hospital, then you are a doctor.”
53. Write the converse of the conditional statement below.
“If you have Canadian coin worth two dollars, then you have a toonie.”
54. Write the converse of the conditional statement below.
“If you make unleavened bread, then you make bread without yeast.”
55. Write the converse of the conditional statement below.
“If an animal is a polar bear, then the animal has white fur.”
56. If the statement below is biconditional, rewrite it in biconditional form. If the statement is not
biconditional, provide a counterexample.
“If you have insomnia, then you cannot sleep at night.”
57. If the statement below is biconditional, rewrite it in biconditional form. If the statement is not
biconditional, provide a counterexample.
“If you work in a hospital, then you are a doctor.”
58. If the statement below is biconditional, rewrite it in biconditional form. If the statement is not
biconditional, provide a counterexample.
“If you have Canadian coin worth two dollars, then you have a toonie.”
59. If the statement below is biconditional, rewrite it in biconditional form. If the statement is not
biconditional, provide a counterexample.
“If you make unleavened bread, then you make bread without yeast.”
60. If the statement below is biconditional, rewrite it in biconditional form. If the statement is not
biconditional, provide a counterexample.
“If an animal is a polar bear, then the animal has white fur.”
61. Show the biconditional statement below is true. If it is not true, give a counterexample.
“A three-dimensional shape is a cube if and only if it has sides all the same length.”
62. Show the biconditional statement below is true. If it is not true, give a counterexample.
“An animal is a vertebrate if and only if it has a spine.”
63. Show the biconditional statement below is true. If it is not true, give a counterexample.
“This month is August if and only if last month was July.”
64. Show the biconditional statement below is true. If it is not true, give a counterexample.
“You are in the capital city of Canada if and only if you are in Ontario.”
65. Show the biconditional statement below is true. If it is not true, give a counterexample.
“I am eating an orange if and only if I am eating a citrus fruit.”
66. Verify the conditional statement below or disprove it with a counterexample.
“If Mother’s Day is this month, then it is May.”
67. Write the converse of the conditional statement below. Verify the converse or disprove it with a
counterexample.
“If Mother’s Day is this month, then it is May.”
68. Write the inverse of the conditional statement below. Verify the inverse or disprove it with a
counterexample.
“If Mother’s Day is this month, then it is May.”
69. Write the contrapositive of the conditional statement below. Verify the contrapositive or disprove
it with a counterexample.
“If Mother’s Day is this month, then it is May.”
70. Verify the conditional statement below or disprove it with a counterexample.
“If the height and radius of a cone and cylinder are the same, then the cone is one third the volume
of the cylinder.”
71. Write the converse of the conditional statement below. Verify the converse or disprove it with a
counterexample.
“If the height and radius of a cone and cylinder are the same, then the cone is one third the volume
of the cylinder.”
72. Write the inverse of the conditional statement below. Verify the inverse or disprove it with a
counterexample.
“If the height and radius of a cone and cylinder are the same, then the cone is one third the volume
of the cylinder.”
73. Write the contrapositive of the conditional statement below. Verify the contrapositive or disprove
it with a counterexample.
“If the height and radius of a cone and cylinder are the same, then the cone is one third the volume
of the cylinder.”
74. Verify the conditional statement below or disprove it with a counterexample.
“If an animal has eight legs, then the animal is a scorpion.”
75. Write the converse of the conditional statement below. Verify the converse or disprove it with a
counterexample.
“If an animal has eight legs, then the animal is a scorpion.”
76. Write the inverse of the conditional statement below. Verify the inverse or disprove it with a
counterexample.
“If an animal has eight legs, then the animal is a scorpion.”
77. Write the contrapositive of the conditional statement below. Verify the contrapositive or disprove
it with a counterexample.
“If an animal has eight legs, then the animal is a scorpion.”
78. Write the converse of the conditional statement below. Verify the converse or disprove it with a
counterexample.
“If x = , then the first decimal of x is 1.”
79. Write the inverse of the conditional statement below. Verify the converse or disprove it with a
counterexample.
“If x = , then the first decimal of x is 1.”
80. Write the contrapositive of the conditional statement below. Verify the contrapositive or disprove
it with a counterexample.
“If x = , then the first decimal of x is 1.”
Problem
1. Two airlines, CanAir (C) and PolarAir (P) fly to the following destinations.
• C = {Yellowknife, Iqaluit, Kelowna, Whitehorse, Calgary, Winnipeg}
• P = {Vancouver, Regina, Prince George, Saskatoon}
a) Illustrate the sets of airline destinations using a Venn diagram.
b) How are C and P related?
2. a) Indicate the multiples of 2 and 3, from 1 to 100, using set notation. List any subsets.
b) Represent the sets and subsets in a Venn diagram.
3. a) Indicate the multiples of 5 and 50, from 1 to 500, using set notation. List any subsets.
b) Represent the sets and subsets in a Venn diagram.
4. a) List 10 of your favourite foods.
b) Organize this information into at least three sets.
c) Display the information in a Venn diagram.
5. a) Determine how many natural numbers from 1 to 100 are
i) odd, square numbers
ii) even, square numbers
iii) not square numbers
b) How many numbers are square?
6. a) Draw a Venn diagram to represent these sets:
• the universal set U = {natural numbers from 1 to 50 inclusive}
• T = {multiples of 3}
• S = {multiples of 6}
• N = {multiples of 19}
b) List the disjoints sets, if there are any.
c) Is each statement true or false? Explain.
i) T  S
ii) S  T
iii) N  N
iv) T = {even numbers from 1 to 50}
v) In this example, the set of natural numbers from 51 to 100 is { }.
7. Consider the following information:
• the universal set U = {set of all integers from –10 to 10}
•XU
•YU
• n(X) = 5
• n(Y) = 6
a) Determine the following:
i) n(U)
ii) n(X)
iii) n(Y)
b) If U = {set of all positive integers from –10 to 10}, how would your answers to part a) change?
8. Consider this universal set:
A = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z}
a) List the following subsets:
• C = {letters that are consonants}
• V = {letters that are vowels}
b) Represent the universal set and subsets in a Venn diagram.
c) Are C and V are disjoints sets? Explain.
9. Consider the following information.
U = {all table games}
C = {card games} or {Hearts, Euchre, Go Fish, Uno, Snap, Set}
S = {card games using a standard deck of cards} or {Hearts, Euchre, Go Fish, Snap}
O = {card games using other decks of cards} or {Uno, Set}
B = {board games} or {chess, checkers, backgammon}
a) Represent this information in a Venn diagram.
b) Name any disjoint sets.
c) Show which sets are subsets of one another using set notation.
d) Checkers, chess and backgammon also all use playing pieces (P). What is the relationship
between set B and set P?
10. A cubic number can be written as x3 for some integer x. Determine how many natural numbers
from 1 to 3000 inclusive are:
a) even and cubic
b) odd and cubic
c) not cubic
11. Paul asked 30 people who saw a movie based on a popular book if they liked the book or the
movie.
• 3 people did not like the movie or the book.
• 15 people liked the movie.
• 22 people liked the book.
Determine how many people liked both the movie and the book, how many liked only the movie,
and how many liked only the book.
12. A sports radio station polled 500 listeners about their favourite sports.
• 245 people listed hockey.
• 213 people listed basketball.
• 84 people did not list hockey or basketball.
Determine how many people listed both hockey and basketball, how many listed hockey but not
basketball, and how many listed basketball but not hockey.
13. Dorothy asked 50 people outside a bookstore if they preferred physical books or electronic readers.
• 2 people said they did not read books.
• 20 people liked both physical books and electronic readers.
• 13 people liked only physical books.
Determine how many people liked only electronic readers.
14. A game store polled 150 customers about whether they preferred to play strategy games or games
of chance.
• 75 people liked to play both.
• 20 people did not like games.
• 31 people liked only strategy games.
Determine how many people liked only games of chance.
15. Noreen asked 65 people at a gym if they liked cycling or running.
• 7 people did not like either activity.
• 24 people liked cycling.
• 40 people liked running.
Determine how many people liked cycling and running.
16. A pet store polled 500 customers about whether they preferred cats or dogs.
• 273 people liked cats.
• 264 people liked dogs.
• 9 people did not like either cats or dogs.
Determine how many people liked cats and dogs.
17. Liam asked 90 people if they preferred tea or coffee.
• 8 people liked both.
• 55 people liked coffee.
• 32 people liked tea.
Determine how many people did not like coffee or tea. Draw a Venn diagram to show your
solution.
18. A restaurant survey asked 300 people if they preferred Indian or Chinese food.
• 146 people liked both.
• 213 people liked Indian food.
• 219 people liked Chinese food.
Determine how many people did not like Indian or Chinese food. Draw a Venn diagram to show
your solution.
19. A camping store surveyed 150 people about the national parks they had visited.
• 91 people had been to Banff National Park in Alberta.
• 77 people had been to Glacier National Park in British Columbia.
• 36 people had not been to either park.
Determine how many people had been to both parks. Draw a Venn diagram to show your solution.
20. A camping store surveyed 450 people about whether they liked to stay in a cabin, a tent, or both.
• 316 people liked a tent.
• 193 people liked a cabin.
• 63 people did not like either option.
Determine how many people liked staying in a tent and a cabin. Draw a Venn diagram to show
your solution.
21. Jamal just moved to Calgary and wants to plant a garden. He likes vegetables and flowers but
wants plants that are easy to care for. Write a set of search instructions Jamal could use to find
online information about gardening in his new city. Use searching tools to narrow down the
number of hits.
22. Consuela lives in Edmonton and misses her mother’s Venezuelan cooking. She will be happy with
any restaurant serving Central American or South American food. She also wants her dinner to
cost less than $20. Write a set or search instructions Consuela could use to find a restaurant she
likes. Use searching tools to narrow down the number of hits.
23. A total of 83 teens attended a performing arts camp to train in at least one of three activities:
dance, acting, or singing.
• 47 took dance, 42 took acting, and 54 took singing.
• 3 took dance and acting only.
• 16 took acting and singing only.
• 19 took dance and singing only.
How many teens trained in all three performing arts?
24. A total of 83 teens attended a performing arts camp to train in at least one of three activities:
dance, acting, or singing.
• 50 took dance, 50 took acting, and 44 took singing.
• 15 took dance and acting only.
• 12 took dance and singing only.
• 69 took acting or singing or both.
• 9 took all three performing arts.
How many teens trained in only one performing art? Use a Venn diagram in your answer.
25. The card game Uno has cards divided into 4 colours: red, blue, green, and yellow. For each colour,
there are 19 number cards and 6 action cards. There are also 8 special black action cards.
Determine the following amounts.
a) n(D), the total number of cards in the deck
b) n(A), the total number of action cards in the deck
c) n(G), the total number of green cards in the deck
d) n(N), the total number of number cards in the deck
e) n(A  G)
f ) n(G  N)
26. Lisa is looking for a book about the solar system for her younger sister, who is 11.
a) What categories and subcategories might she use to refine her search when browsing an online
bookstore?
b) Draw a Venn diagram to represent a search Lisa could use to find a book for her sister.
27. Martin and Louise want to travel from their home in Vancouver to Prince Edward Island.
a) List the types of transportation they could use on their trip.
b) Chose two ways they could travel to PEI. List the subcategories they could choose from for
each method.
c) Draw a Venn diagram to represent one way they could travel to PEI.
d) What are two other things they should consider when choosing how they will travel to PEI?
28. The children’s matching game includes several pairs of identical cards. There are 10 pairs of
animal cards, half with a blue background and half with a red background. There are 8 pairs of
food cards, half with a yellow background and half with a red background. There are also 4 pairs
of people cards with a blue background and 3 pairs of toy cards with a yellow background.
Determine the following amounts.
a) n(D), the total number of cards in the deck
b) n(A), the total number of animal cards in the deck
c) n(R), the total number of red cards in the deck
d) n(B), the total number of blue cards in the deck
e) n(A  B)
f ) n(R  A)
29. A group of 35 tourists can choose between visiting the Aero Space Museum of Calgary, the
Calgary Zoo, or Glenbow Museum.
• 18 went to the Aero Space Museum, 21 went to the zoo, and 23 went to Glenbow Museum.
• 2 went to both museums but not the zoo.
• 3 went to the Aero Space Museum and the zoo only.
• 6 went to Glenbow Museum and the zoo only.
How many tourists went to all three attractions?
30. A group of 50 tourists can choose between visiting the Aero Space Museum of Calgary, the
Calgary zoo, or Glenbow Museum.
• 27 went to the Aero Space Museum, 29 went to the zoo, and 33 went to Glenbow Museum.
• 44 went to at least one museum but not the zoo.
• 9 went to Glenbow Museum only.
• 11 went to all three attractions.
How many tourists went to only two attractions? Use a Venn diagram in your answer.
31. Consider this conditional statement: “If an animal is cold-blooded, then it is an amphibian.”
a) What is the hypothesis? What is the conclusion?
b) Is this statement true? Explain.
c) Write the converse.
d) Is the converse true? Support your decision with a Venn diagram.
32. Consider this conditional statement: “If you speak French and English, then you are bilingual.”
a) What is the hypothesis? What is the conclusion?
b) Is this statement true? Explain.
c) Write the converse.
d) Is the converse true? Explain.
33. Use a truth table to determine whether the following statement is biconditional: “If x2 > 1, then x
is not between –1 and 1.”
34. Use a truth table to determine whether the following statement is biconditional: “If x is a prime
number greater than 2, then x is odd.”
35. Use a truth table to determine whether the following statement is biconditional: “ If
, then x is
greater than 1.”
36. Write the statement below in “if p, then q” form. If the statement is biconditional, rewrite it in
biconditional form. If the statement is not biconditional, provide a counterexample.
“Conifers are trees that produce cones.”
37. Write the statement below in “if p, then q” form. If the statement is biconditional, rewrite it in
biconditional form. If the statement is not biconditional, provide a counterexample.
“A streetcar is a vehicle that runs on rails.”
38. Consider this statement: “You are a member of parliament if and only if you were elected.”
a) Write a conditional statement and its converse.
b) Are the statements you wrote in part a) true or false? Explain how you know.
c) Is the original statement true or false? Explain how you know.
39. Consider this statement: “You can make a phone call if and only if you have a cell phone.”
a) Write a conditional statement and its converse.
b) Are the statements you wrote in part a) true or false? Explain how you know.
c) Is the original statement true or false? Explain how you know.
40. Consider this statement: “You are a juror if and only if you were chosen to be on a jury.”
a) Write a conditional statement and its converse.
b) Are the statements you wrote in part a) true or false? Explain how you know.
c) Is the original statement true or false? Explain how you know.
41. If the converse of a conditional statement is true, what do you know about the inverse? Explain.
42. If a conditional statement is false, what do you know about its contrapositive? Explain.
43. .If a conditional statement is biconditional, what do you know about the statement, and its
converse, inverse, and contrapositive? Explain.
44. Consider this conditional statement:
“If I live in Saskatoon, then I live in Saskatchewan.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
45. Consider this conditional statement:
“If a is negative in the quadratic function y = ax2 + bx + c, then the parabola opens downward.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
46. Consider this conditional statement:
“If a polynomial has three terms, then the polynomial is a trinomial.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
47. Consider this conditional statement:
“If the water is boiling, then it will form steam.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
48. Consider this conditional statement:
“If you invest $1000 for 1 year at 4%, then you will earn $40 in interest.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
49. Consider this conditional statement:
“If
= a, then a < b.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
50. Consider this conditional statement:
“If x is an odd integer, then x2 is an odd perfect square.”
a) Write the converse, the inverse, and the contrapositive.
b) Verify that each statement is true, or disprove it with a counterexample.
venn diagram
Answer Section
MULTIPLE CHOICE
1. ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set | subset | complement
2. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set | disjoint
3. ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
4. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | subset
5. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
6.
7.
8.
9.
10.
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint | subset
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
11.
12.
13.
14.
15.
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | subset | universal set | mutually exclusive
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | subset | universal set
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
16.
17.
18.
19.
20.
21.
22.
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
23.
24.
25.
26.
27.
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
28. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
29. ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
30. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
31. ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
32. ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
33. ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
34.
35.
36.
37.
38.
39.
40.
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
41.
42.
43.
44.
45.
46.
47.
48.
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
49.
50.
51.
52.
53.
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: hypothesis
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: hypothesis
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
54.
55.
56.
57.
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: converse | conditional statement | hypothesis
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse | inverse
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
58.
59.
60.
61.
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
62.
63.
64.
65.
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
66.
67.
68.
69.
70.
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | contrapositive | hypothesis
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | contrapositive | hypothesis
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive | hypothesis
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive | hypothesis
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
71.
72.
73.
74.
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive | inverse | converse
ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
75.
76.
77.
78.
79.
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive
ANS: A
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse | inverse | contrapositive
ANS: B
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse
ANS: D
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive
80. ANS: C
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse | inverse | contrapositive
SHORT ANSWER
1. ANS:
n(L) = 3
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
2. ANS:
n(G) = 10
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
3. ANS:
n(F) = 3
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
4. ANS:
n(L or G) = 13
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
5. ANS:
Sets L and G are disjoint.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint
6. ANS:
L  S, G  S, F  S
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | subset
7. ANS:
Events L and G are mutually exclusive.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | mutually exclusive
8. ANS:
A = {x | 1 < x  50, x  N}
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
9. ANS:
A = {x | 0 < x < 22, x  R}
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
10. ANS:
A = {y | y = 2x, –10  x  –2, x  I}
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element
11. ANS:
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
12. ANS:
S  U, M  U, H  S, G  S
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | subset | universal set
13. ANS:
Set S and set M are disjoint, set H and set G are disjoint.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | disjoint | universal set
14. ANS:
S = {all grade 12 courses that are not social studies}
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | complement | universal set
15. ANS:
Answers may vary. e.g., L = {all language courses} or C = {all science courses}
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: set | element | universal set
16. ANS:
Three students like mathematics and science.
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
17. ANS:
Fifteen students like only mathematics and 12 students like only science.
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
18. ANS:
There are 11 students who plan to ride both the roller coaster and the vertical drop.
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
19. ANS:
There are 14 students who plan to ride only the roller coaster.
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element
20. ANS:
n(X and P) = 2
PTS: 1
DIF: Grade 12
REF: Lesson 3.2
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Exploring Relationships between Sets
KEY: set | element | universal set
21. ANS:
32
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
22. ANS:
20
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
23. ANS:
0
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
24. ANS:
52
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
25. ANS:
12
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
26. ANS:
K  S = {piano}; n(K  S) = 1
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | intersection
27. ANS:
(K  S)´ = {bagpipe, recorder, harmonica, steel drum}
n(K  S)´ = 4
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
28. ANS:
(L  V)´ = {piano, bagpipe, recorder, harmonica, xylophone, steel drum, banjo}
n(L  V)´ = 7
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
29. ANS:
P  M = {bagpipe, recorder, clarinet, flute, xylophone, trumpet, steel drum}
n(P  M) = 7
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
30. ANS:
S = {piano, guitar, violin, cello}
S  B = {violin, cello}
n(S) = 4; (S  B) = 2
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
31. ANS:
(M  K)´ = {guitar, violin, steel drum, banjo}
n(M  K) = 4
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
32. ANS:
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union
33. ANS:
B  C = {chess, Clue, checkers, Go, Scrabble, Monopoly, Hearts, Snap}
B  C = {Clue, Monopoly}
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
34. ANS:
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element
35. ANS:
F  A = {ostrich, emu, penguin, kiwi, snow goose, Arctic tern, osprey, red-tailed hawk}
F  A = {penguin}
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.4 Determine the elements in
the complement, the intersection or the union of two sets. | 2.6 Identify and correct errors in a
given solution to a problem that involves sets. | 2.7 Solve a contextual problem that involves sets,
and record the solution, using set notation. TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
36. ANS:
n(B \ S \ C) = 22%
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
37. ANS:
n((S  C) \ B) = 43%
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
38. ANS:
n((B  S) \ C) = 5%
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
39. ANS:
n(B \ S \ C) + n(S \ B \ C) + n(C \ S \ B) = 63%
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
40. ANS:
n((S  B) \ C) + n((C  S) \ B) + n((B  C) \ S) = 24%
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
41. ANS:
Answers may vary. e.g.,
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
42. ANS:
n(M  B) = 17
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
43. ANS:
94 people travel to work some other way.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
44. ANS:
785 people use public transit only.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
45. ANS:
1056 people use two modes of transportation.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
46. ANS:
n(C  P) = 666
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
47. ANS:
n((D  P) \ C) = 2088
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
48. ANS:
n(D \ P \ C) + n(P \ D \ C) + n(C \ P \ D) = 1686
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
49. ANS:
n(C \ P \ D) = 329
PTS:
1
DIF:
Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
50. ANS:
n(C \ D) = 627
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | intersection | union
51. ANS:
If you cannot sleep at night, then you have insomnia.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
52. ANS:
If you are a doctor, then you work in a hospital.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
53. ANS:
If you have a toonie, then you have a Canadian coin worth two dollars.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
54. ANS:
If you make bread without yeast, then you make unleavened bread.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
55. ANS:
“If an animal has white fur, then the animal is a polar bear.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | converse
56. ANS:
Not biconditional.
Counterexample: There can be other reasons why you cannot sleep at night, such as drinking too
much coffee.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample
57. ANS:
Not biconditional.
Counterexample: Nurses, cleaners, and office staff also work in hospitals.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample
58. ANS:
Biconditional. You have a Canadian coin worth two dollars if and only if you have a toonie.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample
59. ANS:
Biconditional. You make unleavened bread if and only if you make bread without yeast.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample
60. ANS:
Not biconditional.
Arctic foxes and hares have white fur in the winter and are not polar bears.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample
61. ANS:
Converse: If a three-dimensional shape had sides all the same length, then it is a cube. Converse is
false. Biconditional statement is not true. Counterexample: A regular tetrahedron has sides all the
same length.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample | converse
62. ANS:
Conditional statement: If an animal is a vertebrate, then has a spine. Conditional statement is true.
Converse: If an animal has a spine, then it is a vertebrate. Converse is true.
Biconditional statement is true.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample | converse
63. ANS:
Conditional statement: If this month is August, then last month was July. Conditional statement is
true.
Converse: If last month was July, then this month is August Converse is true.
Biconditional statement is true.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample | converse
64. ANS:
Converse: If you are in Ontario, then you are in the capital city of Canada. Converse is false.
Biconditional statement is false. Counterexample: You could be in any other place in Ontario, such
as Toronto, Windsor, or Thunder Bay.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample | converse
65. ANS:
Converse: If I am eating a citrus fruit, then I am eating an orange. Converse is false. Biconditional
statement is false. Counterexample: Limes are also citrus fruit.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | counterexample | converse
66. ANS:
The conditional statement is true. Mother’s Day is always in May.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | counterexample
67. ANS:
Converse: If it is May, then Mother’s Day is this month. The converse is true. May always
contains Mother’s Day.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse | counterexample
68. ANS:
Inverse: If the Mother’s Day is not this month, then it is not May. The inverse is true. Mother’s
Day is only ever in May.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | counterexample
69. ANS:
Contrapositive: If it is not May, then Mother’s Day is not this month. The contrapositive is true.
Mother’s Day is only ever in May.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive | counterexample
70. ANS:
The conditional statement is true.
and
. If r and h have the same value for the cone and the cylinder,
then the cone is one third the volume of the cylinder.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | counterexample
71. ANS:
Converse: If a cone is one third the volume of a cylinder, then the height and radius of the cone
and cylinder are the same.
The converse is false.
Counterexample: A cylinder with r = 3 cm and h = 3 cm has a volume of 84.8 cm3. A cone with r
= 2.325 cm and h = 5 cm has a volume of 28.3 cm3, which is about one third the cylinder’s
volume.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse | counterexample
72. ANS:
Inverse: If the height and radius of a cone and cylinder are not the same, then the cone is not one
third the volume of the cylinder.
The inverse is false.
Counterexample: A cylinder with r = 3 cm and h = 3 cm has a volume of 84.8 cm3. A cone with r
= 2.325 cm and h = 5 cm has a volume of 28.3 cm3, which is about one third the cylinder’s
volume.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | counterexample
73. ANS:
Contrapositive: If a cone is not one third the volume of a cylinder, then the height and radius of the
cone and cylinder are not the same.
The contrapositive is true.
and
. If the cone is not one third the volume of the cylinder, then r
and h cannot have the same value for the cone and the cylinder.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive | counterexample
74. ANS:
The conditional statement is false.
Counterexample: Spiders also have eight legs.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | counterexample
75. ANS:
Converse: If an animal is a scorpion, then it has eight legs.
The converse is true. Scorpions have eight legs.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse | counterexample
76. ANS:
Inverse: If an animal does not have eight legs, then the animal is not a scorpion.
The inverse is true. Spiders have eight legs.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | counterexample
77. ANS:
Contrapositive: If an animal is a not scorpion, then it does not have eight legs.
The contrapositive is false. Counterexample: Spiders have eight legs.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive | counterexample
78. ANS:
Converse: If the first decimal of x is 1, then x = .
The converse is false. Counterexample: x could be
or 0.111...
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | converse | counterexample
79. ANS:
Inverse: If x does not equal , then the first decimal of x is not 1.
The inverse is false. Counterexample: If x is
or 0.111..., then the first decimal is 1.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | counterexample
80. ANS:
Contrapositive: If the first decimal of x is not 1, then x does not equal .
The contrapositive is true. The first decimal in  is 1, so if the first decimal in x is not 1, then x
cannot be .
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive | counterexample
PROBLEM
1. ANS:
a)
b) C and P do not have any common elements so they are disjoint sets.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | disjoint
2. ANS:
a) S = {1, 2, 3, …, 98, 99, 100}
S = {x | 1  x  100, x  N}
D = {2, 4, 6, …, 96, 98, 100}
D = {d | d = 2x, 1  x  50, x  N}
DS
T = {3, 6, 9, …, 93, 96, 99}
T = {t | t = 3x, 1  x  33, x  N}
TS
b)
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | subset
3. ANS:
a) S = {1, 2, 3, …, 498, 499, 500}
S = {x | 1  x  500, x  N}
D = {5, 10, 15, …, 490, 495, 500}
D = {d | d = 5x, 1  x  100, x  N}
DS
T = {50, 100, 150, …, 400, 450, 500}
T = {t | t = 5x, 1  x  10, x  N}
TDS
b)
PTS:
1
DIF:
Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | subset
4. ANS:
Answers may vary. e.g.,
a) spaghetti, pizza, ice cream, strawberries, peaches, mangos, chicken wings, nachos, corn on the
cob, meatball sandwich
b) U = {all types of food}
H = {hot food} or {spaghetti, pizza, chicken wings, nachos, corn on the cob, meatball sandwich}
I = {Italian food} or {spaghetti, pizza, meatball sandwich}
F = {fruit} or {strawberries, peaches, mangos}
c)
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | subset
5. ANS:
a) U = {natural numbers from 1 to 100}
S = {square numbers from 1 to 100}
O = {odd, square numbers from 1 to 100}
E = {even square numbers from 1 to 100}
i) S = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
O = {1, 9, 25, 49, 81}
n(S) = 10
n(O) = 5
There are 10 square numbers from 1 to 100, and 5 of these numbers are odd.
ii) n(E) = n(S) – n(O)
n(E) = 10 – 5
n(E) = 5
There are 5 even, square numbers from 1 to 100.
iii) n(U) = 100
n(S) = n(U) – n(S)
n(S) = 100 – 10
n(S) = 90
There are 90 numbers from 1 to 100 that are not square numbers.
b) There are an infinite number of numbers, so there are an infinite number of square numbers.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | complement | universal set
6. ANS:
a)
b) The disjoints sets are S and N, and T and N.
c) i) False. T is not a subset of S because all multiples of 3 are not multiples of 6.
ii) True. S is a subset of T because all multiples of 6 are multiples of 3.
iii) True. N is a subset of N because all multiples of 19 are multiples of 19.
iv) False. T = {all non-multiples of 3 from 1 to 50}. This set includes odd numbers too.
v) True. The universal set is the natural numbers from 1 to 50 inclusive. So any numbers greater
than 50 are not part of the set and therefore, the set would be empty.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | complement | universal set | disjoint
7. ANS:
a) i) U = {–10, –9, –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
n(U) = 21
Therefore, there are 21 elements in the universal set.
ii) n(X) = n(U) – n(X)
n(X) =21 – 5
n(X) = 16
Therefore, there are 16 elements in the complement of set X.
iii) n(Y) = n(U) – n(Y)
n(Y) =21 – 6
n(Y) = 15
Therefore, there are 15 elements in the complement of set Y.
b) i) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
n(U) = 10
Therefore, there are 10 elements in the universal set.
ii) n(X) = n(U) – n(X)
n(X) =10 – 5
n(X) = 5
Therefore, there are 5 elements in the complement of set X.
iii) n(Y) = n(U) – n(Y)
n(Y) =10 – 6
n(Y) = 4
Therefore, there are 4 elements in the complement of set Y.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | complement | universal set
8. ANS:
a) C = {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
V = {A, E, I, O, U, Y}
b)
c) No, sets C and V are not disjoint because they share the element Y.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | universal set | disjoint
9. ANS:
a)
b) Set S and set O are disjoint. Set C and set B are disjoint.
c) C  U, B  U, S  C  U, O  C  U
d) Set B is equal to set P because they contain the same elements.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | universal set | disjoint
10. ANS:
a) S = {1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744}
n(S) = 14
E = {8, 64, 216, 512, 1000, 1728, 2744}
n(E) = 7
From 1 to 3000, 7 integers are even and cubic.
b) n(S) = 14, n(E) = 7
n(O) = n(S) – n(E)
n(O) = 14 – 7
n(O) = 7
From 1 to 3000, 7 integers are odd and cubic.
c) n(U) = 3000, n(S) = 14
n(S) = n(U) – n(S)
n(S) = 3000 – 14
n(S) = 2986
From 1 to 3000, 2986 integers are not cubic.
PTS: 1
DIF: Grade 12
REF: Lesson 3.1
OBJ: 2.1 Provide examples of the empty set, disjoint sets, subsets and universal sets in context,
and explain the reasoning. | 2.2 Organize information such as collected data and number
properties, using graphic organizers, and explain the reasoning. | 2.3 Explain what a specified
region in a Venn diagram represents, using connecting words (and, or, not) or set notation. | 2.4
Determine the elements in the complement, the intersection or the union of two sets. | 2.6 Identify
and correct errors in a given solution to a problem that involves sets. | 2.7 Solve a contextual
problem that involves sets, and record the solution, using set notation.
TOP: Types of Sets and Set Notation
KEY: element | set | complement | universal set
11. ANS:
Let U represent the universal set. Let M represent the set of people who liked the movie. Let B
represent the set of people who liked the book.
n(M  B) = n(U) – n(M  B)
n(M  B) = 30 – 3
n(M  B) = 27
n(M) + n(B) = 15 + 22
n(M) + n(B) = 37
n(M  B) = 37 – 27
n(M  B) = 10
10 people liked both the book and the movie.
n(M only) = 15 – 10
n(M only) = 5
5 people liked the movie only.
n(B only) = 22 – 10
n(B only) = 12
12 people liked the book only.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
12. ANS:
Let U represent the universal set. Let H represent the set of people who listed hockey. Let B
represent the set of people who listed basketball.
n(H  B) = n(U) – n(H  B)
n(H  B) = 500 – 84
n(H  B) = 416
n(H) + n(B) = 245 + 213
n(H) + n(B) = 458
n(H  B) = 458 – 416
n(H  B) = 42
42 people listed both hockey and basketball.
n(H only) = 245 – 42
n(H only) = 203
203 people listed hockey but not basketball.
n(B only) = 213 – 42
n(B only) = 171
171 people listed basketball but not hockey.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
13. ANS:
Let U represent the universal set. Let R represent the set of people who liked physical books. Let E
represent the set of people who liked electronic readers.
n(E only) = n(U) – n(E  R) – n(R only) – n(E  R)
n(E \ R) = 50 – 2 – 13 – 20
n(E \ R) = 15
15 people like electronic readers only.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
14. ANS:
Let U represent the universal set. Let S represent the set of people who liked strategy games. Let C
represent the set of people who liked games of chance.
n(C \ S) = n(U) – n(C  S) – n(S only) – n(C  S)
n(C \ S) = 150 – 20 – 31 – 75
n(C \ S) = 24
24 people like games of chance only.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
15. ANS:
Let U represent the universal set. Let C represent the set of people who liked cycling. Let R
represent the set of people who liked running.
n(C  R) = n(U) – n(C  R)
n(C  R) = 65 – 7
n(C  R) = 58
n(C  R) = n(C) + n(R) – n(C  R)
n(C  R) = 24 + 40 – 58
n(C  R) = 6
6 people like cycling and running.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
16. ANS:
Let U represent the universal set. Let C represent the set of people who liked cats. Let D represent
the set of people who liked running.
n(C  D) = n(U) – n(C  D)
n(C  D) = 500 – 9
n(C  D) = 491
n(C  D) = n(C) + n(D) – n(C  D)
n(C  D) = 273 + 264 – 491
n(C  D) = 46
46 people like cats and dogs.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
17. ANS:
Let U represent the universal set. Let C represent the set of people who liked coffee. Let T
represent the set of people who liked tea.
n(C \ T) = n(C) – n(C  T)
n(C \ T) = 55 – 8
n(C \ T) = 47
n(T \ C) = n(T) – n(C  T)
n(T \ C) = 32 – 8
n(T \ C) = 24
n(C  T) = n(U) – n(C  T)
n(C  T) = 90 – (47 + 8 + 24)
n(C  T) = 11
11 people did not like coffee or tea.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
18. ANS:
Let U represent the universal set. Let I represent the set of people who liked Indian food. Let C
represent the set of people who liked Chinese food.
n(I \ C) = n(I) – n(I  C)
n(I \ C) = 213 – 146
n(I \ C) = 67
n(C \ I) = n(C) – n(I  C)
n(C \ I) = 219 – 146
n(C \ I) = 73
n(I  C) = n(U) – n(I  C)
n(I  C) = 300 – (146 + 67 + 73)
n(I  C) = 14
14 people did not like Indian or Chinese food.
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
19. ANS:
Let U represent the universal set. Let B represent the set of people who visited Banff National
Park. Let G represent the set of people who visited Glacier National Park.
n(B  G) = n(U) – n(B  G)
n(B  G) = 150 – 36
n(B  G) = 114
n(B  G) = n(B) + n(G)– n(B  G)
n(B  G) = 91 + 77 – 114
n(B  G) = 54
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
20. ANS:
Let U represent the universal set. Let T represent the set of people who like tents. Let C represent
the set of people who like cabins.
n(T  C) = n(U) – n(T  C)
n(T  C) = 450 – 63
n(T  C) = 387
n(T  C) = n(T) + n(C)– n(T  C)
n(T  C) = 316 + 193 – 387
n(T  C) = 122
PTS: 1
DIF: Grade 12
REF: Lesson 3.3
OBJ: 2.2 Organize information such as collected data and number properties, using graphic
organizers, and explain the reasoning. | 2.3 Explain what a specified region in a Venn diagram
represents, using connecting words (and, or, not) or set notation. | 2.7 Solve a contextual problem
that involves sets, and record the solution, using set notation.
TOP: Intersection and Union of Two Sets
KEY: set | element | union | intersection
21. ANS:
Answers may vary. e.g., Jamal needs plants that will survive in southern Alberta, which has a
unique climate. He also wants plants that are easy to grow. He does not say if he wants information
from a website or a book or magazine.
Search instructions: “southern Alberta” OR “Calgary” gardening, easy to grow plants, flowers
AND vegetables
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
22. ANS:
Answers may vary. e.g., I need to search for restaurants in Edmonton. Central and South America
are also referred to as Latin America. I should put quotes around it so I do not get results for
American cuisine.
Search instructions: Edmonton restaurants AND “Latin American” cuisine AND $20
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
23. ANS:
Let x represent the number of teens trained in all three performing arts.
Using the principle of inclusion and exclusion for three sets:
11 teens are studying all three performing arts.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
24. ANS:
Calculate dance only.
n(D \ A \ S): 50 – 15 – 12 – 9 = 14
Record the known numbers on a Venn diagram.
Let x represent the number of teens trained in acting and singing but not dance.
Using the principle of inclusion and exclusion for three sets:
n(A \ D \ S): 50 – 15 – 9 – 16 = 10
n(S \ A \ D): 44 – 12 – 9 – 16 = 7
14 students took dance only, 10 students took acting only, and 7 students took singing only.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
25. ANS:
a) n(D), the total number of cards in the deck: There are 4 colours with 19 number cards and 6
action cards, plus 8 black cards.
4(19 + 6) + 8 = 108
There are 108 cards in the deck.
b) n(A), the total number of action cards in the deck: There are 4 colours with 6 action cards, plus
8 black action cards.
4(6) + 8 = 32
There are 32 action cards.
c) n(G), the total number of green cards in the deck: In green, there are 19 number cards and 6
action cards.
19 + 6 = 25
There are 25 green cards.
d) n(N), the total number of number cards in the deck. There are 4 colours with 19 number cards
each.
4(19) = 76
There are 76 number cards.
e) n(A  G): there are 32 action cards and 25 green cards, but 6 action cards are also green.
32 + 25 – 6 = 51
There are 51 cards that are green or action cards.
f) n(G  N): there are 25 green cards and 76 number cards but only 19 green number cards.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
26. ANS:
Answers may vary. e.g.,
a) Online bookstores offer a lot of products that are not books, so the main category would be
books. Second category could be Science and Nature or some other category that would include
books about the universe. The subcategory of Science and Nature she would want could be
Science or maybe Technology or Nature. Other search categories could include age range, format
(ebook, paperback, hardcover, etc.), price, and so on.
b) Let U = {All books}
A = {Science and Nature books}
B = {Science books}
C = {astronomy books}
D = {books for 9-12 year olds}
X = region showing search results
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
27. ANS:
Answers may vary. e.g.,
a) Martin and Louise could drive, take the train, take the bus, or fly. They could also take the ferry
to PEI or drive over the Confederation Bridge.
b) If they drive, they could use their own car if they have one or they could rent a car. If they rent a
car, they could get an economy or a luxury vehicle. They can drive over the Confederation Bridge
or take a ferry.
If they travel by train, they can stay on the train the whole way or stop over in different cities.
They can get a cabin or berths if they’re staying on the train, or economy or business class seats if
they’re stopping over.
c) They decide to drive their own car and take the ferry.
U = {methods of travel}
A = {car}
B = {own car}
C = {rental car}
D = {ferry}
X = region that represents driving their own car and taking the ferry.
d) They should consider how much money they can afford to spend. Driving or taking the bus are
probably the cheapest modes of transport. They should also consider how much time they have for
their trip. Driving and taking the train are very slow but a good way to see the whole country.
Flying is the fastest mode of travel.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
28. ANS:
a) n(D), the total number of cards in the deck: There are 10 pairs of animal cards, 8 pairs of food
cards, 4 pairs of people cards, and 3 pairs of toy cards.
2(10 + 8 + 4 + 3) = 50
There are 50 cards in the deck.
b) n(A), the total number of animal cards in the deck: There are 10 pairs of animal cards.
2(10) = 20
There are 20 animal cards.
c) n(R), the total number of red cards in the deck: Half of the 20 animal cards are red and half of
the 16 food cards are red.
= 18
There are 18 red cards.
d) n(B), the total number of blue cards in the deck: Half of the 20 animal cards are blue and all of
the 8 people cards are blue.
= 18
There are 18 blue cards.
e) n(A  B): there are 20 animal cards and 18 blue cards, but 10 animal cards are also blue.
20 + 18 – 10 = 28
There are 28 cards that are blue or animal cards.
f) n(R  A): there are 20 animal cards and 18 red cards but only 10 red animal cards.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
29. ANS:
Let x represent the number of tourists who went to all three attractions.
Using the principle of inclusion and exclusion for three sets:
8 tourists went to all three attractions.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
30. ANS:
Zoo only: 50 – 44 = 6
Both museums but not zoo: 27 + 33 – 44 – 11 = 5
Record the numbers on a Venn diagram. Determine x and y.
Glenbow Museum:
Zoo:
Only two attractions: 5 + 8 + 4 = 17
17 tourists went to only two attractions.
PTS: 1
DIF: Grade 12
REF: Lesson 3.4
OBJ: 2.5 Explain how set theory is used in applications such as Internet searches, database
queries, data analysis, games and puzzles. | 2.6 Identify and correct errors in a given solution to a
problem that involves sets. | 2.7 Solve a contextual problem that involves sets, and record the
solution, using set notation.
TOP: Applications of Set Theory
KEY: set | element | union | intersection
31. ANS:
a) Hypothesis: An animal is cold-blooded.
Conclusion: It is an amphibian.
b) The statement is false. Counterexample: Crustaceans and spiders are also cold-blooded.
c) If an animal is an amphibian, then it is cold-blooded.
d) The converse is true. The Venn diagram shows amphibians are animals that are cold-blooded,
but not all cold-blooded animals are amphibians.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | hypothesis | converse
32. ANS:
a) Hypothesis: You speak French and English.
Conclusion: You are bilingual.
b) The statement is true. Being bilingual means you speak two languages.
c) If you are bilingual, you speak French and English.
d) The converse is false. Counterexample: If you are bilingual, you could speak English and
Cantonese.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | hypothesis | converse
33. ANS:
I tested five numbers.
x
p
q
pq
qp
1.5
T
T
T
T
1
F
F
T
T
0.5
F
F
T
T
–0.4
F
F
T
T
–2
T
T
T
T
Both the conditional statement and its converse are always true, so the statement is biconditional.
The statement can be written as: x2 > 1 if and only if x is not between –1 and 1.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
34. ANS:
I tested four numbers.
x
p
q
pq
qp
3
T
T
T
T
5
T
T
T
T
8
F
F
T
T
9
F
T
T
F
11
T
T
T
T
The conditional statement is always true, but its converse is not, so the statement is not
biconditional.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
35. ANS:
I tested three numbers.
x
p
q
pq
qp
T
1
F
F
T
2
T
T
T
T
–2
T
F
F
T
The converse is always true, but the conditional statement is not, so the statement is not
biconditional.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
36. ANS:
Conditional statement: If a tree is a conifer, then it produces cones. This statement is true.
Converse: If a tree produces cones, then it is a conifer. The converse is true. The statement is
biconditional, because the definition of a conifer is a tree that produces cones.
Biconditional statement: A tree is a conifer if and only if it produces cones.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
37. ANS:
Conditional statement: If it is a streetcar, then it is a vehicle that runs on rails.” This statement is
true.
Converse: if it is a vehicle that runs on rails, then it is a streetcar. The converse is false.
Counterexample: A train also runs on rails.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
38. ANS:
a) Conditional statement: If you are a member of parliament, then you were elected.
Converse: If you were elected, then you are a member of parliament.
b) The conditional statement is true. Members of parliament are all elected officials.
The converse is not true. Counterexample: Provincial and city officials are also elected.
c) The original statement is false, because the converse is false. The statement is not biconditional.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
39. ANS:
a) Conditional statement: If can make a phone call, then you have a cell phone.
Converse: If you have a cell phone, then you can make a phone call.
b) The conditional statement is false. You can use a landline, pay phone, or borrow someone else’s
phone.
The converse is not true. Counterexample: The phone may not get reception or the batteries may
be dead.
c) The original statement is false, because the conditional statement and the converse are both
false.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
40. ANS:
a) Conditional statement: If you are a juror, then you were chosen to be on a jury.
Converse: If you were chosen to be on a jury, then you are a juror.
b) The conditional statement is true. You can only be a juror if you are chosen to be on a jury.
The converse is true. If you are chosen to be on a jury, then you are a juror.
c) The original statement is true. The statement is biconditional.
PTS: 1
DIF: Grade 12
REF: Lesson 3.5
OBJ: 3.1 Analyze an “if-then” statement, make a conclusion, and explain the reasoning. | 3.2
Make and justify a decision, using “what if?” questions, in contexts such as probability, finance,
sports, games or puzzles, with or without technology. | 3.3 Determine the converse, inverse and
contrapositive of an “if-then” statement; determine its veracity; and, if it is false, provide a
counterexample. | 3.4 Demonstrate, using examples, that the veracity of any statement does not
imply the veracity of its converse or inverse. | 3.6 Identify and describe contexts in which a
biconditional statement can be justified. | 3.7 Analyze and summarize, using a graphic organizer
such as a truth table or Venn diagram, the possible results of given logical arguments that involve
biconditional, converse, inverse or contrapositive statements.
TOP: Conditional Statements and Their Converse
KEY: conditional statement | biconditional | converse
41. ANS:
If the converse is true, then the inverse will also be true. The inverse and converse are logically
equivalent statements so if one is true the other must also be true.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse
42. ANS:
If the conditional statement is false, then the contrapositive is also false. The conditional statement
and the contrapositive are logically equivalent statements so if on is false the other must also be
false.
PTS:
1
DIF:
Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | contrapositive
43. ANS:
If the conditional statement is biconditional, then the statement, and its converse, inverse, and
contrapositive are all true. For the statement to be biconditional, the statement and its converse
must be true. If the statement is true, this means the contrapositive is also true. If the converse is
true, this means the inverse is also true.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
44. ANS:
a) Converse: If I live is Saskatchewan, then I live in Saskatoon.
Inverse: If I do not live in Saskatoon, then I do not live in Saskatchewan.
Contrapositive: If I do not live is Saskatchewan, then I do not live in Saskatoon.
b) Converse is false. Counterexample: I could live in Moose Jaw.
Inverse is false: Counterexample: If I lived in Moose Jaw, I would live in Saskatchewan.
Contrapositive is true. Since Saskatoon is in Saskatchewan, I cannot live in Saskatoon if I do not
live in Saskatchewan.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
45. ANS:
a) Converse: If the parabola opens downward, then a is negative in the quadratic function y = ax2 +
bx + c.
Inverse: If a is not negative in the quadratic function y = ax2 + bx + c, then the parabola does not
open downward.
Contrapositive: If the parabola doe not open downward, then a is not negative in the quadratic
function y = ax2 + bx + c.
b) Converse is true. For the parabola to open downward, a must be negative.
Inverse is true. If a is positive, then the parabola will open upward.
Contrapositive is true. For the parabola to open downward, a must be negative.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
46. ANS:
a) Converse: If a polynomial is a trinomial, then the polynomial has three terms.
Inverse: If a polynomial does not have three terms, then the polynomial is not a trinomial.
Contrapositive: If a polynomial is not a trinomial, then the polynomial does not have three terms.
b) Converse is true. The definition of a trinomial is a polynomial with three terms.
Inverse is true. If the polynomial does not have three terms, it cannot be a trinomial.
Contrapositive is true. Only trinomials have three terms.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
47. ANS:
a) Converse: If the water forms steam, then it is boiling.
Inverse: If the water is not boiling, then it will not form steam.
Contrapositive: If the water does not form steam, then it is not boiling.
b) Converse is true. Liquid water turns into a gas when it boils.
Inverse is true. Water that is not boiling remains a liquid.
Contrapositive is true. Liquid water must be heated to boiling before it turns into a gas.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
48. ANS:
a) Converse: If you earn $40 in interest, then you have invested $1000 for 1 year at 4%.
Inverse: If you do not invest $1000 for 1 years at 4%, then you will not earn $40 in interest.
Contrapositive: If you do not earn $40 in interest, then you have not invested $1000 for 1 year at
4%.
b) Converse is false. Counterexample: There are many other investments that will earn you $40 in
interest, such as $2000 for 1 year at 2%.
Inverse is false: Counterexample: You could earn $40 in interest with some other investment.
Contrapositive is true. If you do not earn the interest, then you have not made the investment.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
49. ANS:
a) Converse: If a < b, then
= a.
Inverse: If
 a, then a  b.
Contrapositive: If a  b, then
 a.
b) Converse is false. Counterexample: 2 < 5 but
 2.
Inverse is false. Counterexample:
 2, but 2 < 5.
Contrapositive is false. Counterexample: 0.1 > 0.01 and
= 0.1.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive
50. ANS:
a) Converse: If x2 is an odd perfect square, then x is an odd integer.
Inverse: If x is not an odd integer, then x2 is not an odd perfect square.
Contrapositive: If x2 is not an odd perfect square, then x is not an odd integer.
b) Converse is true. If x2 is an odd integer and a perfect square, then x is an odd integer.
Inverse is true. If x is not an odd integer, then x2 cannot be an odd perfect square.
Contrapositive is true. x can only be an odd integer if its square is an odd perfect square.
PTS: 1
DIF: Grade 12
REF: Lesson 3.6
OBJ: 3.3 Determine the converse, inverse and contrapositive of an “if-then” statement; determine
its veracity; and, if it is false, provide a counterexample. | 3.4 Demonstrate, using examples, that
the veracity of any statement does not imply the veracity of its converse or inverse. | 3.5
Demonstrate, using examples, that the veracity of any statement does not imply the veracity of its
contrapositive. | 3.7 Analyze and summarize, using a graphic organizer such as a truth table or
Venn diagram, the possible results of given logical arguments that involve biconditional, converse,
inverse or contrapositive statements.
TOP: The Inverse and the Contrapositive of Conditional Statements
KEY: conditional statement | inverse | converse | contrapositive