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WAEC Further Mathematics 2018 Question 7

Question 7

Sets and Logic

P = {1, 3, 5, 7, 9, 11}, Q = {2, 4, 6, 8, 10, 12} and R = {2, 3, 5, 7, 11} are subsets of U = {1, 2, 3, …, 12}. Which of the following statements is true?

  1. A.Q ∩ R = ∅
  2. B.R ⊂ P
  3. C.(R ∩ P) ⊂ (R ∩ U)
  4. D.n(P′ ∩ R) = 2
Show the answer and explanation

Answer: C ((R ∩ P) ⊂ (R ∩ U))

Explanation

R ∩ P = {3, 5, 7, 11} and R ∩ U = R = {2, 3, 5, 7, 11}, so C is true. Q ∩ R = {2}, 2 ∉ P, and P′ ∩ R = {2} has 1 member.