MATH 105 LMU Set Builder Notation and Numbers Multiple of 2 Question

Exam #2 SET THEORYMATH 105
Name_______________________________________________
Section __________
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 counting number multiple of 2}
A)
B) {4, 6, 8, …}
2) { x
C) {2, 4, 6, …}
x is an even integer smaller than 8}
A) {…, -6, -4, -2, 0, 2, 4, 6}
C) {0, 2, 4, 6}
B) {x | x is an integer between 16 and 21}
D) {17, 18, 19, 20}
4) {9, 12, 15, 18, …, 39}
A) {x | x is a multiple of 3}
C) {x | x is a multiple of 3 between 6 and 42}
B) {x | x is a multiple of 3 greater than 9}
D) {x | x is a multiple of 3 between 9 and 39}
Find n(A) for the set.
5) A = {x | x is a number on a clock face}
A) n(A) = 12
B) n(A) = 3
B) n(A) = 10
1)
2)
B) {…, -6, -4, -2, 2, 4, 6}
D) {2, 4, 6}
Write the set in set-builder notation.
3) {17, 18, 19, 20}
A) {x | x is an integer less than 21}
C) {x | x is an integer between 17 and 20}
6) A = {3, 3, 4, 4, …, 7, 7}
A) n(A) = 3
D) {0, 2, 4, 6, …}
C) n(A) = 24
D) n(A) = 6
C) n(A) = 5
D) n(A) = 6
3)
4)
5)
6)
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}
7) Every element of B is also an element of C.
A) True
B) False
8) A = {x | x is an odd counting number greater than 1 and less than 15}
A) True
B) False
1
7)
8)
Determine whether the statement is true or false.
Let A = {1, 3, 5, 7}
B = {5, 6, 7, 8}
C = {5, 8}
D = {2, 5, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8}
9) C D
A) True
B) False
10) C A
A) True
B) False
9)
10)
Find the number of subsets of the set.
11) {math, English, history, science, art}
A) 16
B) 24
C) 32
D) 28
Find the number of proper subsets of the set.
12) {poetry, drama, speech, art, film}
A) 31
B) 24
C) 32
D) 16
Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set.
13) A = {2, 4, b, d}
A) {1, 2, 4, 5, a, b, c, d, e}
C) {1, 5, a, c, e}
B) {1, 5, a, e}
D) {1, 3, 5, a, c, e}
14) S =
A) ‘
B) {0}
C)
Solve the problem.
15) List all possible subsets of the set {m, n}.
A) {m}, {n},
C) {m}, {n}, {m, n}
B) {m}, {n}
D) {m}, {n}, {m, n},
11)
12)
13)
D) U
14)
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}
C) {q, s, u, w, y, v, w, x, y, z}
B) {w, y}
D) {q, s, u, v, w, x, y, z}
17) A’ B
A) {s, u, w}
C) {q, s, t, u, v, w, x, y}
B) {q, r, s, t, v, x, y, z}
D) {r, s, t, u, v, w, x, z}
2
16)
17)
18) B C
A) {q, s, v, w, x, y, z}
C) {y}
18)
B) {y, z}
D) {w, y, z}
19) A B’
A) {q, s, t, u, v, w, x, y}
C) {r, s, t, u, v, w, x, z}
19)
B) {u, w}
D) {t, v, x}
20) A’ – C
A) {q, s, u, v, x, z}
B) {q, s, u}
C) {r, t}
D) {v, x, z}
21) A (B C)
A) {q, w, y}
B) {q, s, u, w, y, z}
C) {q, y, z}
D) {q, r, w, y, z}
22) B (A – C)
A) {q, r, s, t, u, v, w, x, y}
C) {q, s, u, y, z}
B) {q, s}
D) {q, s, u, y}
For the given sets, construct a Venn diagram and place the elements in the proper region.
23) Let U = {c, d, g, h, k, u, q}
A = {d, h, g, q}
B = {c, d, h, u}
A)
B)
C)
D)
3
20)
21)
22)
23)
24) U = {2, 4, 6, 8, 10, 12}
A = {2, 6, 10}
B = {2, 4, 8}
C = {2, 8, 10, 12}
24)
A)
B)
C)
D)
4
Solve the problem.
25) A survey of a group of 112 tourists was taken in St. Louis. The survey showed the following:
63 of the tourists plan to visit Gateway Arch;
44 plan to visit the zoo;
9 plan to visit the Art Museum and the zoo, but not the gateway Arch;
14 plan to visit the Art Museum and the Gateway Arch, but not the zoo;
16 plan to visit the Gateway Arch and the zoo, but not the Art Museum;
7 plan to visit the Art Museum, the zoo, and the Gateway Arch;
14 plan to visit none of the three places.
How many plan to visit the Art Museum only?
A) 44
B) 14
C) 98
5
D) 32
25)