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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

Let U = {1, 2, ..., 12}, A = {x : x is even}, B = {x : x is a multiple of 3}. What is n(A′ ∩ B′), where complements are taken in U?

By De Morgan's law, A′ ∩ B′ is the complement of A ∪ B. Since n(A ∪ B) = 6 + 4 − 2 = 8, the count is 12 − 8 = 4, namely the elements 1, 5, 7 and 11.

  1. A4
  2. B5Correct
  3. C6
  4. D7

Explanation

A = {2,4,6,8,10,12} has 6 elements, B = {3,6,9,12} has 4, and A ∩ B = {6,12} has 2. n(A ∪ B) = 6 + 4 − 2 = 8. By De Morgan, n(A′ ∩ B′) = 12 − 8 = 4. Hmm, check directly: the elements in neither are 1, 5, 7, 11, which is 4 elements.

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