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Sets and Functions MCQs — Mathematics (page 6)

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.

126. Two circles drawn without overlapping in a Venn diagram show sets that are:

  1. overlapping
  2. equal
  3. subsets of each other
  4. disjoint

Answer: D) disjoint

Explanation: No overlap means no common elements: the sets are disjoint. SLO M-09-A-12 · Understanding

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127. In a Venn diagram of A, B, C inside U, the region inside A and B but outside C is:

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

Answer: D) (A cap B) - C

Explanation: The region inside A and B but outside C is (A cap B) - C. SLO M-09-A-12 · Understanding

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

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

Answer: A) (A cup B) cup C

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

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129. Find the next term of the pattern 2, 6, 12, 20, 30, ldots

  1. 36
  2. 42
  3. 40
  4. 44

Answer: B) 42

Explanation: n(n+1): 1 2, 2 3, ldots, 6 7 = 42. SLO M-09-A-10 · Understanding

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130. A binary relation from A to B is:

  1. always equal to A B
  2. the set A cap B
  3. any subset of A B
  4. the set A cup B

Answer: C) any subset of A B

Explanation: Any subset of the Cartesian product A B is a binary relation from A to B. SLO M-09-A-15 · Knowledge

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131. n(A) = 50, n(B) = 38 and n(A cup B) = 70. Find n(A cap B).

  1. 32
  2. 20
  3. 88
  4. 18

Answer: D) 18

Explanation: n(A cap B) = n(A) + n(B) - n(A cup B) = 50 + 38 - 70 = 18. SLO M-09-A-12 · Understanding

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132. If A = 1, 2, 7, 10, 11, B = 1, 3, 4, 5, 8 and C = 5, 6, 7, 10, find (A cap B) - C.

  1. 6, 9, 12
  2. 1
  3. 5, 7, 10
  4. 1, 7, 10

Answer: B) 1

Explanation: Work out the brackets first. (A cap B) - C = 1. SLO M-09-A-11 · Application

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133. In a town survey of 47 people, 20 speak Urdu at home, 19 speak Punjabi at home and 5 speak both. How many people are in exactly one of the two groups?

  1. 29
  2. 34
  3. 13
  4. 15

Answer: A) 29

Explanation: At least one = 20 + 19 - 5 = 34; first group only = 15; second group only = 14; exactly one = 29; neither = 47 - 34 = 13. So the answer is 29. SLO M-09-A-14 · Application

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134. How many subsets does a set with 4 elements have?

  1. 8
  2. 16
  3. 32
  4. 15

Answer: B) 16

Explanation: Each element is either in or out of a subset, so there are 2^4 = 16 subsets. SLO M-09-A-11 · Application

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135. If n(A) = 2 and n(B) = 5, then n(A B) =

  1. 1024
  2. 10
  3. 7
  4. 32

Answer: B) 10

Explanation: n(A B) = n(A) n(B) = 10. SLO M-09-A-15 · Knowledge

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136. How many proper subsets does a, b, c, d have?

  1. 4
  2. 8
  3. 16
  4. 15

Answer: D) 15

Explanation: There are 2^4 = 16 subsets; leaving out the set itself gives 15 proper subsets. SLO M-09-A-11 · Application

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137. Find the next term of the pattern 3, 7, 11, 15, ldots

  1. 20
  2. 18
  3. 23
  4. 19

Answer: D) 19

Explanation: Add 4 each time: 15 + 4 = 19. SLO M-09-A-10 · Understanding

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138. Which set is always equal to A cup B?

  1. B - A
  2. A cap B
  3. B cup A
  4. A - B

Answer: C) B cup A

Explanation: A cup B = B cup A — the commutative law of union. SLO M-09-A-13 · Application

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139. If U = 1, 2, ldots, 12, A = 1, 3, 5, 6, 11, B = 2, 3, 6, 8, 11 and C = 3, 9, 10, 11, find A' cap C.

  1. 4, 7, 9, 10, 12
  2. 3, 11
  3. 1, 3, 5, 6, 11
  4. 9, 10

Answer: D) 9, 10

Explanation: Work out the brackets first. A' cap C = 9, 10. SLO M-09-A-11 · Application

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140. n(A) = 14, n(B) = 19 and n(A cup B) = 27. Find n(A cap B).

  1. 33
  2. 8
  3. 13
  4. 6

Answer: D) 6

Explanation: n(A cap B) = n(A) + n(B) - n(A cup B) = 14 + 19 - 27 = 6. SLO M-09-A-12 · Understanding

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141. Which relation is a function?

  1. (1, 2), (1, 3), (2, 4)
  2. (1, 2), (2, 3), (3, 3)
  3. (2, 1), (2, 2), (3, 3)
  4. (0, 0), (0, 1)

Answer: B) (1, 2), (2, 3), (3, 3)

Explanation: A function pairs each first element with exactly one second element; the correct one never repeats an x with different y values. SLO M-09-A-16 · Application

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142. In a survey of 60 families: 28 read Jang, 25 read Dawn, 20 read Express; 10 read Jang and Dawn, 8 read Dawn and Express, 6 read Jang and Express, and 3 read all three. How many read only Jang?

  1. 18
  2. 12
  3. 15
  4. 25

Answer: C) 15

Explanation: Only Jang = 28 - 10 - 6 + 3 = 15 (the triple overlap was subtracted twice, so add it back once). SLO M-09-A-14 · Application

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143. How many dots are in the 10th triangular number (1, 3, 6, 10, ldots)?

  1. 45
  2. 100
  3. 50
  4. 55

Answer: D) 55

Explanation: The nth triangular number is n(n+1)2 = 10 112 = 55. SLO M-09-A-10 · Understanding

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

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

Answer: A) De Morgan's law

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

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145. In a class of 46 students, 25 play cricket, 26 play hockey and 11 play both. How many students play cricket only?

  1. 29
  2. 6
  3. 14
  4. 40

Answer: C) 14

Explanation: At least one = 25 + 26 - 11 = 40; first group only = 14; second group only = 15; exactly one = 29; neither = 46 - 40 = 6. So the answer is 14. SLO M-09-A-14 · Application

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146. The point (5, -2) lies in quadrant:

  1. II
  2. IV
  3. III
  4. I

Answer: B) IV

Explanation: Quadrant I: (+, +); II: (-, +); III: (-, -); IV: (+, -). SLO M-09-A-16 · Application

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147. If U = 1, 2, ldots, 12, A = 1, 2, 7, 8, 10, B = 1, 2, 5, 9, 12 and C = 4, 5, 7, 11, find (A cup B)'.

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

Answer: D) 3, 4, 6, 11

Explanation: Work out the brackets first. (A cup B)' = 3, 4, 6, 11. SLO M-09-A-11 · Application

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148. In a class of 26 students, 11 play cricket, 13 play hockey and 4 play both. How many students are in at least one of the two groups?

  1. 7
  2. 20
  3. 6
  4. 16

Answer: B) 20

Explanation: At least one = 11 + 13 - 4 = 20; first group only = 7; second group only = 9; exactly one = 16; neither = 26 - 20 = 6. So the answer is 20. SLO M-09-A-14 · Application

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149. A relation is shown as the ordered pairs (1, 1), (2, 4), (3, 9). In table form the y-row is:

  1. 1, 2, 3
  2. 1, 4, 9
  3. 2, 4, 6
  4. 1, 8, 27

Answer: B) 1, 4, 9

Explanation: The second elements are 1, 4, 9. SLO M-09-A-16 · Application

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150. Which formula gives the nth term of 2, 8, 14, 20, ldots?

  1. 2n+6
  2. 6n-4
  3. 6n+2
  4. 6n-3

Answer: B) 6n-4

Explanation: The terms go up by 6, so the rule is 6n + c. With n = 1: 6 + c = 2, so c = -4 and the rule is 6n-4. SLO M-09-A-10 · Understanding

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