Download sets homework answers

MAT 142
ANSWERS
Sets part 3:
Name:______________________
MAT 142 Summer Session 1
ANSWERS
Homework Day #1:
Name:______________________
I. Sets
Is each set well defined or not well defined?
1. The set of cool cars?
NOT well defined
2. The set of people who have climbed to the top of mount Everest?
Well Defined
Determine whether each set is finite or infinite.
3. The set of even numbers. infinite
4. The set of even numbers between 5 and 1001. finite
5. The set of even natural numbers less than 1001. finite
6. The set of fractions between 0 and 1. infinite
Express each set in Roster Form.
7. The set of natural numbers between 17 and 32. {18,19,20,21,22,23,24,25,26,27,28,29,30,31,32}

8. A  x
9.
x  4  12
{16}
B   x x  N and x is odd 
Express each set in set-builder notation.
{1,3,5,7,…}
10.
A  7,8,9,10,11,12
x
x  N and 7  x  12
11.
B  4,8,12,16, 20,...
x
x  N and x even greater than 2
Write a description of each set.
12.
A  1, 2,3, 4,5
The set of natural numbers less than six.
13.
B  1, 4,9,16, 25,...
The set of the squares of the natural numbers.
14.
S  Monday, Tuesday,Wednesday, Thursday, Friday, Saturday, Sunday
The set of the days of the week
State whether each statement is true or false.
e a, e, i, o, u
16. e a, e, i, o, u
17. h a, e, i, o, u
15.

18. 4  x
False
True
False
x  N and x is even
For problems 19 – 21 use A  1,3,5, 7
19. Find n(A)
20. Find n(B)
21. Find n(C)
False
B 

C  x x  N 
4
0

For problems 22 – 24 determine if the pair of sets are equal, equivalent, both or neither.
22.
A  Bob, Sue, Julie B  Julie, Bob, Sue
BOTH
23. A is the set of letters in the word college B is the set of letters in the word algebra
NEITHER
24. A is the set of NFL teams
B is the set of Superbowl winning NFL teams
Give a written description of three sets that YOU are an element of.
25.
26.
27.
NEITHER
(Answers will vary by individual student)
II. Subsets.
True or False
28.
29.
30.
31.
32.
33.
3  1, 2,3, 4,5
3  1, 2,3, 4,5
3 1, 2,3, 4,5
  1, 2,3, 4,5
   1, 2,3, 4,5
 
False
True
True
False
True
True

True
35. 1, 2,3, 4,5  1, 2,3, 4,5 False
34.
36.
37.
38.
39.
1, 2,3, 4,5  1, 2,3, 4,5 True
True
  ,1, 2,3, 4,5
True
,1, 2,3, 4,5
True
  ,1, 2,3, 4,5

Given A  x
x is a sport that uses a ball  and B   football , soccer, tennis are the following
statements true or false?
40. A  B
False
41. A  B
False
42.
43.
44.
B A
B A
AB
True
True
False
45. List all of the subsets of
A  a, b, c
,a ,b ,c ,a, b , a, c , b, c, a, b, c
46. WITHOUT listing the subsets, HOW MANY subsets would
B  a, b, c, d , e, f  have? SHOW how you
obtained your answer!!!!
n(B) = 6 so B will have 26 subsets and 26 = 64
III. Venn Diagrams and Set Operations.
For questions 1 – 10 use the Venn Diagram. In questions 1 – 5 list the set of elements in roster form.
U
A
B
2
10
A  B 1, 2,3, 4,5,6,7,8,9
2. A  B
2
3. A  B
10
4. A  B
2,3,5,7,10
1.
 B  A   B  A 10
5.
For questions 6 – 10 indicate whether the statement is True or False.

6. A  B  x

7. B  x
x is an even prime number
x is a prime number
True
False
B  A  A
False
9. B   x x is a prime number True
8.
10.
B  A
False
For questions 11 – 17 use
CD
12. C  D
13. C  D
14. C  D
11.
C  1, 2,3 D  1, 2
1,1 ; 1, 2 ;  2,1 ;  2, 2 ; 3,1 ; 3, 2
3
1, 2,3
D or 1, 2
1,1 ; 1, 2 ; 1,3 ;  2,1 ; 2, 2 ; 2,3
C or
DC
16. Does C  D  D  C ?
NO
17. Does n  C  D   n  D  C  ?
15.

For questions 18 – 21 use U  x
YES
x  N and x  11 O   x x  N and x is odd and x  11
E   x x  N and x is even and x  10
18.
19.
20.
21.
OE
OE
S   x x  N and x  7

1, 2,3, 4,5,6,7,8,9
 E  S  7,9,10
O  E  S 1, 2,3, 4,5,6,7,9
22. A group of 35 GCC students who spoke either Spanish or French or both were surveyed. It was found that 14
students speak French and 4 speak both French and Spanish. How many speak Spanish? (Hint: Use
n  A  B   n  A  n  B   n  A  B  )
35 = 14
+
?
- 4
so n(B) = 25
so 25 students speak Spanish.
IV. Venn Diagrams with three sets.
23. Construct a Venn Diagram illustrating the following sets.
U  a, b, c, d , e, f , g , h, i, j A  c, d , e, g , h, i B  a, c, d , g C  c, f , i, j
Answer:
U
B
d g
c
i
A
C
b
Given the following Venn Diagram, answer questions 24 – 30
U
B
6
3
8
4
5
7
A
11
13
A B
25. A  B
26. A  B 
24.
27.
28.
29.
30.
C
15
1, 2,3, 4,5,6,7,8,9,12,14
3, 4,5
1, 7,9
 A  C 
2,11,12,13,14,15
A   B  C  3, 4,5,7
AB C
1,3, 4,5,6,7,8,9
 A  B    B  C  2,3, 4,5,6,7,8,12,14
Given the following Venn Diagram with regions marked I – VIII, determine whether the following statements in
questions 31 – 34 are true or false. Show some work!
U
A
II
VI
V
IV
C
B
VIII
31.
A   B  C    A  B   A  C 
 I , II ,V ,VI   II , III , IV ,V ,VI ,VII 
 II ,V  VI ,V 
II ,V ,VI
II ,V ,VI
TRUE
32.
A   B  C   A   B  C  
 I    I ,VI ,VII ,VIII   I , II , III ,VIII  
 I   I ,VIII 
 I , II ,V ,VI   I ,VIII 
I
I
TRUE
33.
A   B  C   A   B  C 
 I , II ,V ,VI   I , II , III ,VI ,VII ,VIII 
 I , II , III ,V ,VI ,VII ,VIII 
 III , IV ,VII ,VIII   II , III , IV , V , VI , VII 
 III , IV ,VII 
FALSE
34.
 A  B   B  C   B   A  C 
 I , II , III , IV ,V ,VI   II , III , IV ,V ,VI ,VII 
 II , III , IV ,V ,VI 
 II , III , IV ,V  V ,VI 
 II , III , IV ,V ,VI 
TRUE
Use set statements to describe the shaded area shown in the Venn Diagrams of problems 35 and 36.
35.
A B
OR
A B
U
A
36.
B
C
B
A
U
OR
B
A
C
A
A
B
C