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Sets, Combinatorics, and Probability
53. Let S = A × B where A = {2, 3, 4} and B = {3, 5}. Which of the following statements are true?
a. A # S
d. (5, 4) [ S
b. 3 [ S
e. [ # S
c. (3, 3) [ S
f. {(2, 5)} # S
54. Let
A = {x 0 x is a word that appears before dog in an English language dictionary}
B = {x 0 x is a word that appears after canary in an English language dictionary}
C = {x 0 x is a word of more than four letters}
Which of the following statements are true?
a. B # C
b. A c B = {x 0 x is a word in an English language dictionary}
c. cat [ B d C ′
d. bamboo [ A − B
55. Consider the following subsets of ℤ:
A = {x 0 (E y)( y [ ℤ and y ≥ 4 and x = 3y)}
B = {x 0 (E y)( y [ ℤ and x = 2y)}
C = {x 0 x [ ℤ and 0 x 0 ≤ 10}
Using set operations, describe each of the following sets in terms of A, B, and C.
a. set of all odd integers
b. {−10, −8, −6, −4, −2, 0, 2, 4, 6, 8, 10}
c. {x 0 (E y)( y [ ℤ and y ≥ 2 and x = 6y)}
d. {−9, −7, −5, −3, −1, 1, 3, 5, 7, 9}
e. {x 0 (E y)( y [ ℤ and y ≥ 5 and x = 2y + 1)} c {x 0 (E y)( y [ ℤ and y ≤ −5 and x = 2y − 1)}
56. Let
A = {x 0 x [ ℝ and 1 < x ≤ 3}
B = {x 0 x [ ℝ and 2 ≤ x ≤ 5}
Using set operations, describe each of the sets shown in terms of A and B.
a.
0
1
2
3
4
0
1
2
3
4
0
1
2
3
4
b.
c.