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Sets and Functions MCQs — Mathematics (page 3)

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.

51. The relation “is less than” on A = 1, 2, 3 is:

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

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

Explanation: List every pair (a, b) with a < b: (1, 2), (1, 3), (2, 3). SLO M-09-A-16 · Application

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52. If A subseteq B, then A cup B =

  1. A cap B
  2. varnothing
  3. B
  4. A

Answer: C) B

Explanation: Everything in A is already in B, so the union is B. SLO M-09-A-11 · Application

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53. Which set is always equal to A - B?

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

Answer: B) A cap B'

Explanation: A - B = A cap B' — the difference written with a complement. SLO M-09-A-13 · Application

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54. Find the next term of the pattern 1, 1, 2, 3, 5, 8, ldots

  1. 11
  2. 13
  3. 16
  4. 12

Answer: B) 13

Explanation: Fibonacci pattern: each term is the sum of the two before it, 5 + 8 = 13. SLO M-09-A-10 · Understanding

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55. n(A) = 25, n(B) = 18, n(A cap B) = 7. How many elements are in A only?

  1. 18
  2. 11
  3. 36
  4. 25

Answer: A) 18

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

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56. Verify the De Morgan's law: with U = 1, 2, ldots, 10, A = 3, 7, 8, 9, 10, B = 4, 6, 7, 8, C = 4, 6, 7, 9, both (A cup B)' and A' cap B' equal:

  1. 7
  2. 4, 6, 7, 9
  3. 3, 4, 6, 7, 8, 9, 10
  4. 1, 2, 5

Answer: D) 1, 2, 5

Explanation: Working out each side separately gives the same set 1, 2, 5, which verifies (A cup B)' = A' cap B'. SLO M-09-A-13 · Application

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57. Out of 34 patients, 12 have fever, 19 have a cough and 5 have both. How many patients are in exactly one of the two groups?

  1. 26
  2. 8
  3. 7
  4. 21

Answer: D) 21

Explanation: At least one = 12 + 19 - 5 = 26; first group only = 7; second group only = 14; exactly one = 21; neither = 34 - 26 = 8. So the answer is 21. SLO M-09-A-14 · Application

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58. How many subsets does a set with 5 elements have?

  1. 32
  2. 25
  3. 10
  4. 31

Answer: A) 32

Explanation: Each element is either in or out of a subset, so there are 2^5 = 32 subsets. SLO M-09-A-11 · Application

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59. If A = 1, 2, 3, the relation R = (x, y) : y = x + 1, x, y in A is:

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

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

Explanation: Both x and y must be in A, so (3, 4) is not allowed. SLO M-09-A-15 · Knowledge

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60. If A = 3, 4, 8, 9, 12, B = 3, 4, 7, 9, 12 and C = 2, 4, 7, 11, find A - (B cup C).

  1. 4, 7
  2. 3, 4, 7, 8, 9, 12
  3. 4
  4. 8

Answer: D) 8

Explanation: Work out the brackets first. A - (B cup C) = 8. SLO M-09-A-11 · Application

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

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

Answer: D) 2, 5, 6

Explanation: Work out the brackets first. (A cup B) cap C = 2, 5, 6. SLO M-09-A-11 · Application

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62. The point where a graph crosses the y-axis always has:

  1. x = 0
  2. x = 1
  3. y = 0
  4. x = y

Answer: A) x = 0

Explanation: Points on the y-axis have x-coordinate 0. SLO M-09-A-16 · Application

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63. The relation y = 2x + 1 on the domain 0, 1, 2, 3 written as ordered pairs is:

  1. (1, 0), (3, 1), (5, 2), (7, 3)
  2. (0, 2), (1, 4), (2, 6), (3, 8)
  3. (0, 1), (1, 3), (2, 5), (3, 7)
  4. (0, 0), (1, 1), (2, 2), (3, 3)

Answer: C) (0, 1), (1, 3), (2, 5), (3, 7)

Explanation: Substitute each x: (0, 1), (1, 3), (2, 5), (3, 7). SLO M-09-A-16 · Application

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64. If A B = (a, 1), (a, 2), (b, 1), (b, 2), then B =

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

Answer: D) 1, 2

Explanation: The second elements form B = 1, 2. SLO M-09-A-15 · Knowledge

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65. In a survey of 100 families: 50 read Jang, 40 read Dawn, 30 read Express; 15 read Jang and Dawn, 10 read Dawn and Express, 12 read Jang and Express, and 5 read all three. How many read none of them?

  1. 88
  2. 12
  3. 13
  4. 17

Answer: B) 12

Explanation: At least one = 50 + 40 + 30 - 15 - 10 - 12 + 5 = 88, so none = 100 - 88 = 12. SLO M-09-A-14 · Application

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66. How many subsets does a set with 3 elements have?

  1. 7
  2. 9
  3. 8
  4. 6

Answer: C) 8

Explanation: Each element is either in or out of a subset, so there are 2^3 = 8 subsets. SLO M-09-A-11 · Application

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67. If A = 3, 4 and B = 5, then A B =

  1. (5, 3), (5, 4)
  2. (3, 5)
  3. (3, 5), (4, 5)
  4. 3, 4, 5

Answer: C) (3, 5), (4, 5)

Explanation: A B is the set of all ordered pairs (a, b) with a in A, b in B: (3, 5), (4, 5). SLO M-09-A-15 · Knowledge

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68. Which point lies on the graph of x + y = 7?

  1. (1, 6)
  2. (3, 5)
  3. (2, 4)
  4. (7, 1)

Answer: A) (1, 6)

Explanation: Substitute: (1, 6) satisfies x + y = 7; the others do not. SLO M-09-A-16 · Application

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69. Out of 43 patients, 22 have fever, 27 have a cough and 10 have both. How many patients have neither symptom?

  1. 12
  2. 4
  3. 29
  4. 39

Answer: B) 4

Explanation: At least one = 22 + 27 - 10 = 39; first group only = 12; second group only = 17; exactly one = 29; neither = 43 - 39 = 4. So the answer is 4. SLO M-09-A-14 · Application

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70. In a town survey of 46 people, 21 speak Urdu at home, 23 speak Punjabi at home and 11 speak both. How many people speak Urdu only (not Punjabi)?

  1. 33
  2. 10
  3. 13
  4. 22

Answer: B) 10

Explanation: At least one = 21 + 23 - 11 = 33; first group only = 10; second group only = 12; exactly one = 22; neither = 46 - 33 = 13. So the answer is 10. SLO M-09-A-14 · Application

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71. Verify the distributive law of union over intersection: with A = 1, 2, 5, 6, 7, B = 1, 5, 7, 10, C = 2, 3, 5, 7, both A cup (B cap C) and (A cup B) cap (A cup C) equal:

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

Answer: C) 1, 2, 5, 6, 7

Explanation: Working out each side separately gives the same set 1, 2, 5, 6, 7, which verifies A cup (B cap C) = (A cup B) cap (A cup C). SLO M-09-A-13 · Application

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72. n(A) = 16, n(B) = 22 and n(A cap B) = 9. Find n(A cup B).

  1. 29
  2. 7
  3. 47
  4. 38

Answer: A) 29

Explanation: n(A cup B) = n(A) + n(B) - n(A cap B) = 16 + 22 - 9 = 29. SLO M-09-A-12 · Understanding

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73. n(A) = 15, n(B) = 18, n(C) = 12, n(A cap B) = 5, n(B cap C) = 6, n(A cap C) = 4 and n(A cap B cap C) = 2. Find n(A cup B cup C).

  1. 30
  2. 28
  3. 32
  4. 45

Answer: C) 32

Explanation: n(A cup B cup C) = 15 + 18 + 12 - 5 - 6 - 4 + 2 = 32. SLO M-09-A-12 · Understanding

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74. The statement A cup (B cap C) = (A cup B) cap (A cup C) is the:

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

Answer: B) distributive law of union over intersection

Explanation: It is the distributive law of union over intersection. SLO M-09-A-13 · Application

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75. If A = 1, 2, then A A =

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

Answer: A) (1, 1), (1, 2), (2, 1), (2, 2)

Explanation: Pair every element with every element, including itself. SLO M-09-A-15 · Knowledge

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