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Sets and Functions MCQs — Mathematics (page 5)

155 multiple-choice questions on Sets and Functions from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

101. On a graph, the points (1, 2), (2, 4), (3, 6) all lie on the line:

  1. y = x + 1
  2. y = x^2
  3. x = 2y
  4. y = 2x

Answer: D) y = 2x

Explanation: Each y is twice its x. SLO M-09-A-16 · Application

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102. n(A) = 25, n(B) = 18 and n(A cap B) = 7. Find n(A cup B).

  1. 43
  2. 18
  3. 36
  4. 50

Answer: C) 36

Explanation: n(A cup B) = n(A) + n(B) - n(A cap B) = 25 + 18 - 7 = 36. SLO M-09-A-12 · Understanding

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103. The vertical-line test is used on a graph to decide whether a relation is:

  1. a function
  2. linear
  3. a set
  4. an inverse

Answer: A) a function

Explanation: If any vertical line meets the graph more than once, some x has two y values, so it is not a function. SLO M-09-A-16 · Application

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104. If n(A) = 4 and n(B) = 4, then n(A B) =

  1. 8
  2. 65536
  3. 16
  4. 256

Answer: C) 16

Explanation: n(A B) = n(A) n(B) = 16. SLO M-09-A-15 · Knowledge

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105. n(A) = 30, n(B) = 25 and n(A cup B) = 45. Find n(A cap B).

  1. 20
  2. 15
  3. 10
  4. 55

Answer: C) 10

Explanation: n(A cap B) = n(A) + n(B) - n(A cup B) = 30 + 25 - 45 = 10. SLO M-09-A-12 · Understanding

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106. Given 11^2 = 121 and 111^2 = 12321, the pattern suggests 1111^2 =

  1. 12344321
  2. 1233321
  3. 123321
  4. 1234321

Answer: D) 1234321

Explanation: The digits rise to the number of ones and fall again: 1111^2 = 1234321. SLO M-09-A-10 · Understanding

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107. In a Venn diagram of A, B, C inside U, the region inside A only is:

  1. A - B
  2. A cup (B cap C)
  3. A - (B cup C)
  4. A cap B'

Answer: C) A - (B cup C)

Explanation: The region inside A only is A - (B cup C). SLO M-09-A-12 · Understanding

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108. n(A) = 34, n(B) = 21, n(A cap B) = 12. How many elements are in A only?

  1. 34
  2. 43
  3. 9
  4. 22

Answer: D) 22

Explanation: A only = n(A) - n(A cap B) = 34 - 12 = 22. SLO M-09-A-12 · Understanding

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109. Which set is always equal to A cap (B cup C)?

  1. (A cap B) cup C
  2. (A cup B) cap (A cup C)
  3. A cap B cap C
  4. (A cap B) cup (A cap C)

Answer: D) (A cap B) cup (A cap C)

Explanation: A cap (B cup C) = (A cap B) cup (A cap C) — the distributive law of intersection over union. SLO M-09-A-13 · Application

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110. n(A) = 20, n(B) = 25, n(C) = 30, n(A cap B) = 8, n(B cap C) = 10, n(A cap C) = 6 and n(A cap B cap C) = 3. Find n(A cup B cup C).

  1. 75
  2. 48
  3. 54
  4. 51

Answer: C) 54

Explanation: n(A cup B cup C) = 20 + 25 + 30 - 8 - 10 - 6 + 3 = 54. SLO M-09-A-12 · Understanding

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111. The statement (A cap B)' = A' cup B' is the:

  1. De Morgan's law
  2. distributive law of union over intersection
  3. distributive law of intersection over union
  4. associative law of union

Answer: A) De Morgan's law

Explanation: It is the De Morgan's law. SLO M-09-A-13 · Application

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112. Verify the distributive law of intersection over union: with A = 2, 3, 5, 6, 10, B = 2, 3, 4, 10, C = 2, 4, 6, 9, both A cap (B cup C) and (A cap B) cup (A cap C) equal:

  1. 2, 3, 4, 5, 6, 9, 10
  2. 2
  3. 2, 4, 6
  4. 2, 3, 6, 10

Answer: D) 2, 3, 6, 10

Explanation: Working out each side separately gives the same set 2, 3, 6, 10, which verifies A cap (B cup C) = (A cap B) cup (A cap C). SLO M-09-A-13 · Application

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113. Using the pattern 1 = 1^2, 1 + 3 = 2^2, 1 + 3 + 5 = 3^2, ldots, find the sum of the first 20 odd numbers.

  1. 400
  2. 39
  3. 420
  4. 440

Answer: A) 400

Explanation: The sum of the first n odd numbers is n^2, so the answer is 20^2 = 400. SLO M-09-A-10 · Understanding

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114. In a Venn diagram of A, B, C inside U, the region inside all three sets is:

  1. A cup B cup C
  2. A cap B
  3. (A cap B) - C
  4. A cap B cap C

Answer: D) A cap B cap C

Explanation: The region inside all three sets is A cap B cap C. SLO M-09-A-12 · Understanding

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115. If A = 3, 4, 5, 6, 10, B = 4, 6, 8, 10, 11 and C = 4, 5, 6, 7, find A cap (B cup C).

  1. 4, 5, 6, 10
  2. 3, 4, 5, 6, 10
  3. 3, 4, 5, 6, 7, 8, 10, 11
  4. 10

Answer: A) 4, 5, 6, 10

Explanation: Work out the brackets first. A cap (B cup C) = 4, 5, 6, 10. SLO M-09-A-11 · Application

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116. The relation y = x2 on the domain 2, 4, 6 written as ordered pairs is:

  1. (1, 2), (2, 4), (3, 6)
  2. (2, 2), (4, 4), (6, 6)
  3. (2, 2), (4, 3), (6, 4)
  4. (2, 1), (4, 2), (6, 3)

Answer: D) (2, 1), (4, 2), (6, 3)

Explanation: Substitute each x: (2, 1), (4, 2), (6, 3). SLO M-09-A-16 · Application

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117. If A = 7, 8, 9, 10, 11, B = 1, 2, 9, 10, 12 and C = 2, 5, 8, 10, find A cap B cap C.

  1. 10
  2. 8, 9, 10
  3. 3, 4, 5, 6
  4. 2, 8, 10

Answer: A) 10

Explanation: Work out the brackets first. A cap B cap C = 10. SLO M-09-A-11 · Application

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118. For non-empty sets A neq B, which is true?

  1. A B neq B A
  2. A B = B A
  3. n(A B) = n(A) + n(B)
  4. A B = A cup B

Answer: A) A B neq B A

Explanation: Ordered pairs depend on order: (1, a) neq (a, 1), so in general A B neq B A. SLO M-09-A-15 · Knowledge

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119. Mathematics is best described as the study of:

  1. only shapes
  2. only numbers and calculations
  3. patterns, structures and relationships
  4. memorising formulas

Answer: C) patterns, structures and relationships

Explanation: Numbers, shapes, change and data all show patterns and structure; mathematics studies these and the relationships between them. SLO M-09-A-10 · Understanding

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120. Find the next term of the pattern 1, 8, 27, 64, ldots

  1. 81
  2. 100
  3. 125
  4. 216

Answer: C) 125

Explanation: Cube numbers n^3: 5^3 = 125. SLO M-09-A-10 · Understanding

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121. In a class of 43 students, 17 play cricket, 26 play hockey and 8 play both. How many students are in exactly one of the two groups?

  1. 9
  2. 35
  3. 27
  4. 8

Answer: C) 27

Explanation: At least one = 17 + 26 - 8 = 35; first group only = 9; second group only = 18; exactly one = 27; neither = 43 - 35 = 8. So the answer is 27. SLO M-09-A-14 · Application

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122. Find the next term of the pattern 1, 4, 9, 16, 25, ldots

  1. 49
  2. 36
  3. 35
  4. 30

Answer: B) 36

Explanation: These are square numbers n^2: the next is 6^2 = 36. SLO M-09-A-10 · Understanding

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123. If A = 1, 2 and B = a, b, then A B =

  1. (1, a), (2, b)
  2. (1, a), (1, b), (2, a), (2, b)
  3. 1, 2, a, b
  4. (a, 1), (a, 2), (b, 1), (b, 2)

Answer: B) (1, a), (1, b), (2, a), (2, b)

Explanation: A B is the set of all ordered pairs (a, b) with a in A, b in B: (1, a), (1, b), (2, a), (2, b). SLO M-09-A-15 · Knowledge

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124. In a survey of 44 shoppers at a mall, 21 bought clothes, 21 bought shoes and 12 bought both. How many shoppers are in exactly one of the two groups?

  1. 30
  2. 9
  3. 18
  4. 14

Answer: C) 18

Explanation: At least one = 21 + 21 - 12 = 30; first group only = 9; second group only = 9; exactly one = 18; neither = 44 - 30 = 14. So the answer is 18. SLO M-09-A-14 · Application

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125. In a class of 51 students, 20 play cricket, 21 play hockey and 5 play both. How many students play neither game?

  1. 10
  2. 36
  3. 15
  4. 31

Answer: C) 15

Explanation: At least one = 20 + 21 - 5 = 36; first group only = 15; second group only = 16; exactly one = 31; neither = 51 - 36 = 15. So the answer is 15. SLO M-09-A-14 · Application

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