1106Ch2TestReview
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School
Miami Dade College, Miami *
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Course
1105
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
8
Uploaded by EarlUniversePony13
Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
List the elements in the set.
1)
{x | x is a whole number between 4 and 8}
A)
{4, 5, 6, 7, 8}
B)
{5, 6, 7}
C)
{4, 5, 6, 7}
D)
{5, 6, 7, 8}
1)
Write the set in set
-
builder notation.
2)
{40, 45, 50, 55, ..., 90}
A)
{x | x is a multiple of 5 between 40 and 90}
B)
{x | x is a multiple of 5}
C)
{x | x is a multiple of 5 between 35 and 95}
D)
{x | x is a multiple of 5 greater than 40}
2)
3)
{2, 4, 8, 16, 32, ...}
A)
{x
x is a positive multiple of 2}
B)
{x
x is a positive integer power of 2}
C)
{x
x is an integer power of 2}
D)
{x
x is a positive multiple of 4}
3)
Identify the set as finite or infinite.
4)
{x | x is a fraction between 16 and 17}
A)
Infinite
B)
Finite
4)
5)
{x | x is a prime number}
A)
Infinite
B)
Finite
5)
Find n(A) for the set.
6)
A =
{x | x is a month in the year}
A)
n(A) =
1
B)
n(A) =
24
C)
n(A) =
52
D)
n(A) =
12
6)
7)
A =
{
-
5, -
4, -
3, ..., 0}
A)
n(A) =
4
B)
n(A) =
5
C)
n(A) =
6
D)
n(A) =
1
7)
Determine whether or not the set is well defined.
8)
{x | x is a low
-
fat ice cream}
A)
Not well defined
B)
Well defined
8)
9)
{x | x is a tennis player who has won at Wimbledon}
A)
Well defined
B)
Not well defined
9)
1
Write true or false for the following statement.
Let A =
{3, 5, 7, 9, 11, 13}
B =
{3, 5, 9, 11}
C =
{5, 9, 13}
10)
Every element of C is also an element of A.
A)
True
B)
False
10)
Decide whether ⊆
, ⊂
, both, or neither can be placed in the blank to make a true statement.
11)
{8, 9, 10} {8, 9, 10}
A)
⊆
B)
Both ⊂
and ⊆
C)
Neither
D)
⊂
11)
Find the number of subsets of the set.
12)
{math, English, history, science, art}
A)
32
B)
28
C)
24
D)
16
12)
Find the number of proper subsets of the set.
13)
{car, boat, truck, train}
A)
8
B)
15
C)
14
D)
16
13)
Let U =
{1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set.
14)
T =
{1, 2, 5, b, d}
A)
{4, a, c, e}
B)
{3, 4, a, b, c, e}
C)
{3, 4, a, c, e}
D)
{4, a, b, c, e}
14)
Solve the problem.
15)
List all possible proper subsets of the set {2, 6, 7}.
A)
{2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}
B)
{2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}, {2, 6, 7}
C)
∅
, {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}, {2, 6, 7}
D)
∅
, {2}, {6}, {7}, {2, 6}, {2, 7}, {6, 7}
15)
List the elements in the set .
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}.
16)
A ∪
C
A)
{q, s, u, v, w, y, z}
B)
{w, y}
C)
{q, s, u, v, w, x, y, z}
D)
{q, s, u, w, y, v, w, x, y, z}
16)
17)
A ∩
B'
A)
{u, w}
B)
{r, s, t, u, v, w, x, z}
C)
{q, s, t, u, v, w, x, y}
D)
{t, v, x}
17)
2
18)
(A ∩
B)'
A)
{t, v, x}
B)
{q, s, t, u, v, w, x, y}
C)
{r, t, u, v, w, x, z}
D)
{s, u, w}
18)
19)
A ∪
(B ∩
C)
A)
{q, y, z}
B)
{q, r, w, y, z}
C)
{q, w, y}
D)
{q, s, u, w, y, z}
19)
20)
B ∩
(A -
C)
A)
{q, s}
B)
{q, s, u, y}
C)
{q, r, s, t, u, v, w, x, y}
D)
{q, s, u, y, z}
20)
21)
(A ∩
B') ∪
(B ∩
A')
A)
{u, w, y, z}
B)
{q, s, y}
C)
{q, s, u, w, y, z}
D)
{u, w, z}
21)
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.
22)
n(A ∩
B) =
n(B ∩
A)
A)
True
B)
False
22)
Find the Cartesian product.
23)
A =
{13, 11, 5}
B =
{5, 8}
Find A ×
B.
A)
{(13, 5), (13, 8), (11, 5), (11, 8), (5, 5), (5, 8)}
B)
{(13, 5), (11, 8)}
C)
{(5, 13), (5, 11), (5, 5), (8, 13), (8, 11), (8, 5)}
D)
{(13, 5), (11, 5), (5, 5)}
23)
24)
A =
{2, 3, 9, 7}
B =
{0, 1}
Find B ×
A.
A)
{0, 1, 2, 3, 9, 7}
B)
{(2, 0), (3, 0), (9, 0), (7, 0), (2, 1), (3, 1), (9, 1), (7, 1)}
C)
{(2, 0), (2, 1), (3, 0), (3, 1)}
D)
{(0, 2), (0, 3), (0, 9), (0, 7), (1, 2), (1, 3), (1, 9), (1, 7)}
24)
Find the indicated cardinal number.
25)
Find n(D ×
B) given that B =
{1, 3} and D =
{7, 8, 9, 10}.
A)
12
B)
8
C)
16
D)
7
25)
26)
Find n(C ×
D) given that C =
{4, 5, 6} and D =
{7, 8, 9, 10}.
A)
7
B)
27
C)
81
D)
12
26)
3
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For the given sets, construct a Venn diagram and place the elements in the proper region.
27)
Let U =
{c, d, g, h, k, u, q}
A =
{d, h, g, q}
B =
{c, d, h, u}
A)
B)
C)
D)
27)
4
28)
Let U =
{1, 2, 3, 4, 5, 6, 7, 8}
A =
{3, 6, 8}
B =
{4, 6}
C =
{1, 6, 7, 8}
A)
B)
C)
D)
28)
Write a description of the shaded region using the symbols A, B, C, ∪
, ∩
, -
, and
′
as needed.
29)
A)
A -
B
B)
(A ∩
B)
′
C)
A ∪
B
D)
A
′
∩
B
′
29)
Decide whether the given statement is always true or not always true.
30)
A ∩
A
′
=
∅
A)
Not always true
B)
Always true
30)
5
31)
(A ∪
B) ⊆
A
A)
Always true
B)
Not always true
31)
Write a description of the shaded region using the symbols A, B, C, ∪
, ∩
, -
, and
′
as needed.
32)
A)
B -
A
′
B)
B ∩
A
′
C)
A -
B
D)
A ∩
B
′
32)
Decide whether the given statement is always true or not always true.
33)
(A ∩
B) ⊆
B
A)
Not always true
B)
Always true
33)
Describe the conditions under which the statement is true.
34)
A ∩
B =
A
A)
A ⊆
B
B)
B ⊆
A
C)
B =
∅
D)
Always true
34)
Find the cardinal number of the set.
35)
The numbers in the Venn Diagram below represent cardinalities.
Find n(A ∪
B).
A)
52
B)
24
C)
48
D)
4
35)
36)
The numbers in the Venn Diagram below represent cardinalities.
Find n(A ∩
B').
A)
20
B)
4
C)
24
D)
28
36)
6
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Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region.
37)
n(A) =
14, n(B) =
21, n(A ∪
B) =
25, n(B
′
) =
9
A)
B)
C)
D)
37)
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.
38)
n(A ∪
B) =
n(A) +
n(B) -
n(A ∩
B)
A)
True
B)
False
38)
7
Answer Key
Testname: 1106CH2TESTREVIEW
1) B
2) C
3) B
4) A
5) A
6) D
7) C
8) A
9) A
10) A
11) A
12) A
13) B
14) A
15) D
16) C
17) A
18) C
19) D
20) A
21) D
22) A
23) A
24) D
25) B
26) D
27) C
28) D
29) D
30) B
31) B
32) B
33) B
34) A
35) C
36) C
37) D
38) A
8