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Quiz Chapter 4: Operations on Sets

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

Question 1 of 10Score: 0

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?

Full Question List & Answer Key

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

1. 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.

2. 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.

3. 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 (∅).

4. 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}.

5. Which set theoretical symbol represents the statement 'element x belongs to both set P and set Q'?

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

The intersection symbol ∩ means 'AND', indicating that x belongs to both set P and set Q simultaneously.

6. 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.

7. 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}.

8. Given n(ξ) = 50, n(A) = 28, n(B) = 22, and n(A ∪ B)' = 6. Find n(A ∩ B).

  1. A. 6
  2. B. 8
  3. C. 10
  4. D. 12
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Answer: A

n(A ∪ B) = 50 - 6 = 44. Using n(A ∪ B) = n(A) + n(B) - n(A ∩ B): 44 = 28 + 22 - n(A ∩ B) ⇒ n(A ∩ B) = 50 - 44 = 6.

9. Given set A = {2, 3, 5, 7} and set B = {1, 3, 5, 9}. Find A ∩ B.

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

The intersection A ∩ B consists of elements that are common to both set A and set B. The common elements are 3 and 5.

10. 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}.

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