Download Sample

Chapter 2 Exam A
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Let U = {all soda pops}; A = {all diet soda pops}; B = {all cola soda pops}; C = {all soda pops in cans}; and
D = {all caffeine-free soda pops}. Describe the given set in words.
1) A ∩ B ∩ D
A) All diet, all cola, and all caffeine-free soda pops
B) All diet, caffeine-free, cola soda pops
C) All soda pops not in cans
D) All diet, caffeine-free, cola soda pops in cans
Shade the Venn diagram to represent the set.
2) C' ∩ (A ∪ B)
A)
2)
B)
Write a description of the shaded region using the symbols A, B, C, ∪, ∩, -, and ′ as needed.
3)
A) B ∩ (A ∩ C)′
1)
B) B - (A ∩ C)
Determine whether the set is well defined or not.
4) {x : x is a four-year college in Oregon}
A) Well defined
C) A′ ∩ C′ ∩ B
3)
D) B′ - (A ∪ B)
4)
B) Not well defined
Page 11
Find the cardinal number of the indicated set by referring to the given table.
5) A - (F ∪ S),
given the following table:
U.S. Production (in Thousands of Tons) of Certain Nuts
Year
Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H)
1993 (T)
184
584
232
41
1994 (F)
99
585
232
21
1995 (V)
134
304
234
39
1996 (S)
111
412
205
17
A) 888
B) 997
C) 757
5)
D) 173
Determine whether the set is well defined or not.
6) {x :x is a football team that has won the Super Bowl}
A) Not well defined
B) Well defined
Find n(A) for the set.
7) A = {{a, b}, {c, d}, {e, b}}
A) n(A) = 5
C) n(A) = 3
D) n(A) = 2
Use set notation to list all the elements of the set.
8) The integers from 4 to 8 inclusive
A) {5, 6, 7}
B) {4, 5, 6, 7}
C) {4, 5, 6, 7, 8}
D) {5, 6, 7, 8}
Find the number of subsets of the set.
9) {13, 14, 15}
A) 6
B) 3
C) 7
D) 8
6)
7)
B) n(A) = 6
8)
9)
Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the natural numbers
and the given set. Be sure to indicate the general correspondence.
10) {9, 14, 19, 24, 29, ...}
A) 1, 2, 3, 4, 5, ...,
n, ...
B)
↕
↕ ↕ ↕ ↕
↕
9, 14, 19, 24, 29, ..., 4n - 3, ...
C) 1, 2, 3, 4, 5, ...,
n, ...
D)
↕ ↕ ↕ ↕ ↕
↕
9, 14, 19, 24, 29, ..., 5n + 4, ...
10)
1,
↕
9,
1,
↕
9,
2, 3, 4, 5, ...,
↕ ↕ ↕ ↕
14, 19, 24, 29, ...,
2, 3, 4, 5, ...,
↕ ↕ ↕ ↕
14, 19, 24, 29, ...,
Identify the set as finite or infinite.
11) The set of people watching fireworks at Miller Park on July 4, 2000 at 9:45 P.M.
A) Finite
B) Infinite
n, ...
↕
4n + 4, ...
n, ...
↕
5n + 3, ...
11)
Page 12
Use the Venn diagram below to find the number of elements in the region.
12) n((C ∪ B) - (A ∪ B))
A) 2
12)
B) 11
C) 5
D) 15
C) n, o
D) o
Determine which labeled sections make up the indicated set.
13) B - C
A) v, p
13)
B) n, o, p
Decide whether the statement is true or false.
14) {2, 22, 36, 44} ⊆ {2, 4, 6, 8, ..., 98}
A) False
B) True
Decide whether the sets are equal.
15) {4, 8, 12, 16, 32} and {4, 8, 12, 16, ..., 32}
A) Yes
B) No
14)
15)
Find the cardinal number of the indicated set by referring to the given table.
16) V ∩ (P ∪ W),
given the following table:
U.S. Production (in Thousands of Tons) of Certain Nuts
Year
Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H)
1993 (T)
182
584
232
41
1994 (F)
99
583
232
21
1995 (V)
134
304
234
39
1996 (S)
111
412
205
19
A) 368
B) 343
C) 158
Identify the set as finite or infinite.
17) The set of odd numbers greater than 1000
A) Finite
16)
D) 0
17)
B) Infinite
Page 13
Use an alternative method to express the set.
18) {x: x has bike trails}
The table shows some of the facilities available at selected State Parks in New Jersey.
hiking
bike visitor
camping trails boating swimming trails center
Allaire
yes
yes
no
yes
no yes
Parvin
yes
yes
yes
yes
no yes
Delaware and Raritan Canal no
yes
yes
yes
yes no
Corson's Inlet
no
yes
yes
no
no no
Wharton Forest
yes
yes
yes
yes
no yes
A) {Delaware and Raritan Canal}
B) (Delaware and Raritan Canal)
C) ∅
D) {Allaire, Parvin, Corson's Inlet, Wharton Forest}
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
19) (A ∪ B)'
A) {r, s, t, u, v, w, x, z}
C) {r, t, v, x}
B) {s, u, w}
D) {t, v, x}
Use set notation to list all the elements of the set.
20) The integers between 4 and 8, not inclusive
B) {4, 5, 6, 7, 8}
A) {5, 6, 7}
C) {5, 6, 7, 8}
18)
19)
20)
D) {4, 5, 6, 7}
Page 14
Answer Key
Test Name: Chapter 2 Exam A
1) B
2) B
3) C
4) A
5) A
6) B
7) C
8) C
9) D
10) C
11) A
12) D
13) C
14) B
15) B
16) A
17) B
18) A
19) C
20) A
Page 15
Chapter 2 Exam B
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or
false.
1) n(A ∩ B) = n(B ∩ A)
1)
A) True
B) False
Shade the Venn diagram to represent the set.
2) (A ∩ B ∩ C')'
A)
2)
B)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
List the subsets.
3) List all of the three element subsets of the set {a, b, c, d, e}.
3)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or
false.
4) n(A ∩ B) = n(A) - n(B)
4)
A) True
B) False
Page 16
Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the natural numbers
and the given set. Be sure to indicate the general correspondence.
5) {1, 5, 9, 13, 17, ...}
A) 1, 2, 3, 4, 5, ...,
n, ...
B) 1, 2, 3, 4, 5,
↕ ↕ ↕ ↕ ↕
↕
↕ ↕ ↕ ↕ ↕
1, 5, 9, 13, 17, ..., 3n + 1, ...
1, 5, 9, 13, 17,
C) 1, 2, 3, 4, 5, ...,
n, ...
D) 1, 2, 3, 4, 5,
↕ ↕ ↕ ↕ ↕
↕
↕ ↕ ↕ ↕ ↕
1, 5, 9, 13, 17, ..., 3n - 1, ...
1, 5, 9, 13, 17,
Find n(A) for the set.
6) A = {∅, 0}
A) n(A) = 0
5)
...,
n, ...
↕
...,4n - 3, ...
...,
n, ...
↕
..., 4n + 3, ...
6)
B) n(A) = 2
C) n(A) = 1
D) n(A) = ∅
Use the Venn diagram below to find the number of elements in the region.
7) n(A ∩ C)
A) 37
7)
B) 2
C) 10
D) 18
Show that the set has cardinal number ℵ0 by establishing a one-to-one correspondence between the natural numbers
and the given set. Be sure to indicate the general correspondence.
1 3 5 7 9
8)
, , , ,
...
3 5 7 9 11
8)
A) 1,
↕
1
,
3
2,
↕
3
,
5
3,
↕
5
,
7
4,
↕
7
,
9
5, ...,
n, ...
↕
↕
9
n+1
, ... ,
, ...
11
3n - 1
B) 1,
↕
1
,
3
2,
↕
3
,
5
3,
↕
5
,
7
4,
↕
7
,
9
C)
2,
↕
3
,
5
3,
↕
5
,
7
4, 5, ...,
n, ...
↕
↕
↕
7 9
2n - 1
,
, ... ,
, ...
9 11
2n + 1
D) 1,
↕
1
,
3
2,
↕
3
,
5
3,
↕
5
,
7
4, 5, ...,
n, ...
↕
↕
↕
7 9
2n + 1
,
, ... ,
, ...
9 11
2n - 1
1,
↕
1
,
3
5, ...,
n, ...
↕
↕
9
3n - 1
, ... ,
, ...
11
n+1
Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or
false.
9) If B ⊆ A, n(B) = n(A) - n(A - B).
9)
A) True
B) False
Find the number of subsets of the set.
10) {0}
A) 4
B) 2
10)
C) 1
D) 0
Page 17
Let U = {q, r, s, t, u, v, w, x, y, z}
A = {q, s, u, w, y}
B = {q, s, y, z}
C = {v, w, x, y, z}. List the elements in the set.
11) A ∪ (B ∩ C)
A) {q, y, z}
B) {q, s, u, w, y, z}
11)
C) {q, w, y}
D) {q, r, w, y, z}
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
List the subsets.
12) List all of the three element subsets of the set {a, b, c, d}.
12)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the cardinal number of the indicated set by referring to the given table.
13) V ∩ (P ∪ W),
given the following table:
U.S. Production (in Thousands of Tons) of Certain Nuts
Year
Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H)
1993 (T)
182
584
232
41
1994 (F)
99
583
232
21
1995 (V)
134
304
234
39
1996 (S)
111
412
205
19
A) 158
B) 368
C) 343
Decide whether the sets are equivalent.
14) {∅} and {x : x is a state in the U.S. with a minimum voting age of 51}
A) Yes
B) No
13)
D) 0
14)
Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is true or
false.
15) n(A ∪ B) + n(A ∩ B) = n(A) + n(B)
15)
A) True
B) False
Use the following definitions to determine if the statement is true or false.
N = {x : x is a natural number}
I = {x : x is an integer}
R = {x : x is a real number}
W = {x : x is a whole number}
Q = {x : x is a rational number}
16) I is a proper subset of Q and R.
A) True
B) False
Identify the set as finite or infinite.
17) The set of odd numbers greater than 1000
A) Finite
B) Infinite
Decide whether the statement is true or false.
18) ∅ ⊆ {6, 12, 18, 24, 30}
A) False
B) True
16)
17)
18)
Page 18
Use the following definitions to determine if the statement is true or false.
N = {x : x is a natural number}
I = {x : x is an integer}
R = {x : x is a real number}
W = {x : x is a whole number}
Q = {x : x is a rational number}
19) I is a proper subset of N, W, Q, and R.
A) True
B) False
Find, if possible, the number of elements in sets A, B, and C using the given information.
20) n(A - C) = 12
n(C - A) = 4
n(A ∪ C) = 22
n(A ∩ B) = 10
n((C ∩ A) - B) = 2
n((A ∩ B) - C) = 6
n(B - (A ∪ C)) = 3
n(B ∩ C) = 6
A) n(A) = 12, n(B) = 21, n(C) = 10
B) n(A) = 18, n(B) = 15, n(C) = 10
C) n(A) = 10, n(B) = 25, n(C) = 18
D) The information is inconsistent or incomplete.
19)
20)
Page 19
Answer Key
Test Name: Chapter 2 Exam B
1) A
2) B
3) {a, b, c}, {a, b, d}, {a, b, e}, {a, c, d}, {a, c, e}, {a, d, e}, {b, c, d}, {b, c, e}, {b, d, e}, {c, d, e}
4) B
5) B
6) B
7) C
8) C
9) A
10) B
11) B
12) {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}
13) B
14) B
15) A
16) A
17) B
18) B
19) B
20) B
Page 20