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Quiz Chapter 4: Operations on Sets

10 questions · Form 4 Mathematics Bab 3: Operations on Sets

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Given sets A = {1, 2, 3}, B = {2, 3, 4}, and C = {3, 4, 5}. Find (A ∩ B) ∪ C.

  1. A. {2, 3, 4, 5}
  2. B. {3}
  3. C. {1, 2, 3, 4, 5}
  4. D. {2, 3}
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Answer: A

First, evaluate the brackets: A ∩ B = {2, 3}. Next, take the union with set C: {2, 3} ∪ {3, 4, 5} = {2, 3, 4, 5}.

2. If set A and set B are disjoint sets (A ∩ B = ∅), what is n(A ∩ B)?

  1. A. 0
  2. B. 1
  3. C. Infinity
  4. D. Undefined
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Answer: A

Disjoint sets have no common elements, meaning their intersection is the empty set (∅), so n(A ∩ B) = 0.

3. In a survey of 30 pupils, 18 like Mathematics (M) and 15 like Science (S). If 5 like neither, how many like BOTH Mathematics and Science?

  1. A. 8
  2. B. 10
  3. C. 12
  4. D. 3
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Answer: A

n(M ∪ S) = 30 - 5 = 25 pupils. n(M ∩ S) = n(M) + n(S) - n(M ∪ S) = 18 + 15 - 25 = 8 pupils.

4. Given the universal set ξ = {1, 2, 3, 4, 5, 6, 7, 8} and set P = {2, 4, 6, 8}. Find P'.

  1. A. {2, 4, 6, 8}
  2. B. {1, 3, 5, 7}
  3. C. {1, 2, 3, 4}
  4. D. {5, 6, 7, 8}
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Answer: B

The complement P' consists of all elements in the universal set ξ that are NOT in set P. Thus P' = {1, 3, 5, 7}.

5. In a class of 40 students, 25 play football, 20 play badminton, and 8 play both games. How many students do NOT play either game?

  1. A. 3
  2. B. 5
  3. C. 7
  4. D. 12
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Answer: A

Total playing at least one game n(F ∪ B) = 25 + 20 - 8 = 37. Students playing neither = 40 - 37 = 3.

6. Given set K = {factors of 12} and set L = {factors of 18}. Find n(K ∩ L).

  1. A. 2
  2. B. 3
  3. C. 4
  4. D. 6
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Answer: C

K = {1, 2, 3, 4, 6, 12} and L = {1, 2, 3, 6, 9, 18}. The intersection K ∩ L = {1, 2, 3, 6}. Therefore, n(K ∩ L) = 4.

7. Given A ⊂ B (A is a subset of B). What is A ∪ B?

  1. A. A
  2. B. B
  3. C. ∅
  4. D. ξ
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Answer: B

Since set A is entirely contained within set B, combining all elements of A and B yields set B.

8. Given ξ = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4}. Find A' ∩ B'.

  1. A. {5}
  2. B. {1, 2, 3, 4}
  3. C. {1, 2, 5}
  4. D. ∅
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Answer: A

A' = {3, 4, 5} and B' = {1, 2, 5}. The intersection A' ∩ B' = {5}. (By De Morgan's Law, A' ∩ B' = (A ∪ B)' = {5}).

9. Which expression describes the shaded region outside sets A, B, and C inside the universal set ξ?

  1. A. A ∩ B ∩ C
  2. B. (A ∪ B ∪ C)'
  3. C. A' ∩ B' ∩ C
  4. D. (A ∩ B ∩ C)'
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Answer: B

The region outside all three sets combined (A ∪ B ∪ C) is the complement of their union, denoted as (A ∪ B ∪ C)'.

10. Given set A = {x : x is a letter in 'KSSM'}. Find n(A).

  1. A. 4
  2. B. 3
  3. C. 2
  4. D. 1
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Answer: B

Sets do not contain duplicate elements. Set A = {'K', 'S', 'M'}, so n(A) = 3.

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