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Sets and Functions MCQs — Mathematics

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.

1. The pattern of even numbers 2, 4, 6, 8, ldots has the general term:

  1. 2n + 1
  2. 2n
  3. n + 2
  4. n^2

Answer: B) 2n

Explanation: The nth even number is 2n. SLO M-09-A-10 · Understanding

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

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

Answer: D) distributive law of intersection over union

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

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3. If A = 3, 6, 8, 10, 11, B = 3, 7, 9, 10, 11 and C = 4, 5, 10, 11, find A cup (B cap C).

  1. 3, 6, 8, 10, 11
  2. 3, 4, 5, 6, 7, 8, 9, 10, 11
  3. 4, 5, 7, 9, 10, 11
  4. 3, 10, 11

Answer: A) 3, 6, 8, 10, 11

Explanation: Work out the brackets first. A cup (B cap C) = 3, 6, 8, 10, 11. SLO M-09-A-11 · Application

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4. If A = 1, 2, 4, 9, 10, B = 1, 4, 6, 8, 10 and C = 4, 8, 9, 10, find A cap B cap C.

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

Answer: A) 4, 10

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

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5. The graph of a relation is the set of points (1, 5), (2, 5), (3, 5). These points lie on:

  1. a horizontal line
  2. the line y = x
  3. a vertical line
  4. the x-axis

Answer: A) a horizontal line

Explanation: All have y = 5, so they lie on the horizontal line y = 5. SLO M-09-A-16 · Application

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6. The domain of the relation R = (2, 5), (3, 5), (4, 7) is:

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

Answer: C) 2, 3, 4

Explanation: The domain is the set of first elements of the ordered pairs. SLO M-09-A-15 · Knowledge

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7. A circle for A drawn completely inside the circle for B shows that:

  1. A = U
  2. A subseteq B
  3. B subseteq A
  4. A cap B = varnothing

Answer: B) A subseteq B

Explanation: Every element of A is also in B. SLO M-09-A-12 · Understanding

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

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

Answer: A) associative law of intersection

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

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9. If n(A) = 3 and n(B) = 4, then n(A B) =

  1. 4096
  2. 7
  3. 12
  4. 81

Answer: C) 12

Explanation: n(A B) = n(A) n(B) = 12. SLO M-09-A-15 · Knowledge

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10. 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 only Jang?

  1. 45
  2. 35
  3. 23
  4. 28

Answer: D) 28

Explanation: Only Jang = 50 - 15 - 12 + 5 = 28 (the triple overlap was subtracted twice, so add it back once). SLO M-09-A-14 · Application

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11. Find the next term of the pattern 2, 4, 8, 16, 32, ldots

  1. 64
  2. 48
  3. 34
  4. 62

Answer: A) 64

Explanation: Each term doubles: 32 2 = 64. SLO M-09-A-10 · Understanding

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12. A music playlist has 38 songs: 20 are qawwalis, 19 are pop songs and 12 are tagged as both. How many songs are qawwalis only?

  1. 27
  2. 8
  3. 11
  4. 15

Answer: B) 8

Explanation: At least one = 20 + 19 - 12 = 27; first group only = 8; second group only = 7; exactly one = 15; neither = 38 - 27 = 11. So the answer is 8. SLO M-09-A-14 · Application

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13. Which formula gives the nth term of 5, 8, 11, 14, ldots?

  1. 5n+3
  2. 3n+2
  3. 3n+5
  4. 3n+3

Answer: B) 3n+2

Explanation: The terms go up by 3, so the rule is 3n + c. With n = 1: 3 + c = 5, so c = 2 and the rule is 3n+2. SLO M-09-A-10 · Understanding

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14. The range of the relation R = (2, 5), (3, 5), (4, 7) is:

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

Answer: B) 5, 7

Explanation: The range is the set of second elements of the ordered pairs. SLO M-09-A-15 · Knowledge

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15. If A = 6, 8, 9, 10, 11, B = 1, 2, 5, 6, 10 and C = 5, 6, 10, 11, find (A cup B) cap C.

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

Answer: D) 5, 6, 10, 11

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

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16. Every point on the x-axis has:

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

Answer: D) y = 0

Explanation: On the x-axis the height (the y-coordinate) is 0. SLO M-09-A-16 · Application

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17. If (2, 3) in A B, then:

  1. 2 in B only
  2. 2 in A and 3 in B
  3. 3 in A and 2 in B
  4. 2, 3 in A only

Answer: B) 2 in A and 3 in B

Explanation: In A B the first element comes from A and the second from B. SLO M-09-A-15 · Knowledge

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18. In the multiplication table, the numbers on the diagonal 1, 4, 9, 16, ldots are:

  1. prime numbers
  2. square numbers
  3. even numbers
  4. cube numbers

Answer: B) square numbers

Explanation: They are 1 1, 2 2, 3 3, ldots SLO M-09-A-10 · Understanding

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19. If n(A) = 2 and n(B) = 3, how many binary relations are there from A to B?

  1. 64
  2. 63
  3. 6
  4. 32

Answer: A) 64

Explanation: A relation is any subset of A B, which has 6 elements, so there are 2^6 = 64 relations. SLO M-09-A-15 · Knowledge

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20. If A = 4, 8, 9, 10, 12, B = 2, 3, 8, 9, 12 and C = 2, 3, 5, 8, find A cup B cup C.

  1. 2, 3, 4, 5, 8, 9, 10, 12
  2. 1, 5, 6, 7, 11
  3. 2, 3, 8
  4. 2, 3, 5

Answer: A) 2, 3, 4, 5, 8, 9, 10, 12

Explanation: Work out the brackets first. A cup B cup C = 2, 3, 4, 5, 8, 9, 10, 12. SLO M-09-A-11 · Application

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21. If A = 2, 8, 10, 11, 12, B = 2, 3, 5, 6, 12 and C = 2, 6, 8, 9, find (B - A) cup C.

  1. 2
  2. 2, 6, 8
  3. 2, 3, 5, 6, 8, 9
  4. 10, 11

Answer: C) 2, 3, 5, 6, 8, 9

Explanation: Work out the brackets first. (B - A) cup C = 2, 3, 5, 6, 8, 9. SLO M-09-A-11 · Application

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22. Which point lies on the graph of y = 3x - 2?

  1. (1, 2)
  2. (2, 5)
  3. (1, 1)
  4. (0, 2)

Answer: C) (1, 1)

Explanation: Substitute: (1, 1) satisfies y = 3x - 2; the others do not. SLO M-09-A-16 · Application

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23. In a Venn diagram of A, B, C inside U, the region inside A or B (or both) is:

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

Answer: A) A cup B

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

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24. The range of the relation R = (-1, 1), (0, 0), (1, 1), (2, 4) is:

  1. 0, 1, 4
  2. -1, 0, 1, 2
  3. 1, 4
  4. -1, 0, 1, 2, 4

Answer: A) 0, 1, 4

Explanation: The range is the set of second elements of the ordered pairs. SLO M-09-A-15 · Knowledge

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25. 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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