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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 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}).

2. 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}.

3. Given universal set ξ = {x : x is an integer, 1 ≤ x ≤ 10}, set A = {2, 4, 6, 8, 10}, and set B = {3, 6, 9}. Find (A ∩ B)'.

  1. A. {6}
  2. B. {1, 2, 3, 4, 5, 7, 8, 9, 10}
  3. C. {2, 3, 4, 8, 9, 10}
  4. D. {1, 5, 7}
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Answer: B

A ∩ B = {6}. Therefore, (A ∩ B)' includes all elements in ξ except 6, which is {1, 2, 3, 4, 5, 7, 8, 9, 10}.

4. 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.

5. 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: A

If set A is entirely contained within set B (A ⊂ B), all elements of A are in B. Thus, the intersection of A and B is set A itself.

6. Given ξ = {1, 2, 3, 4, 5, 6, 7}, P = {1, 3, 5}, Q = {2, 3, 4}. Find (P ∪ Q)'.

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

P ∪ Q = {1, 2, 3, 4, 5}. The complement (P ∪ Q)' consists of remaining elements in ξ, which are {6, 7}.

7. Given set M = {a, b, c} and set N = {c, d, e}. What is A ∪ B?

  1. A. {c}
  2. B. {a, b, d, e}
  3. C. {a, b, c, d, e}
  4. D. {a, b, c, c, d, e}
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Answer: C

The union M ∪ N contains all unique elements present in set M, set N, or both, which gives {a, b, c, d, e}.

8. 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.

9. 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.

10. Given sets P = {red, blue}, Q = {yellow, blue}, and R = {green, red}. Find P ∩ Q ∩ R.

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

There is no single color present in all three sets simultaneously. Thus, P ∩ Q ∩ R is the empty set (∅).

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