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

Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5, 6} and B = {4, 5, 6, 7, 8}. What is the number of elements in (A ∪ B)′, the complement of A ∪ B?

The complement of A ∪ B has 2 elements. The union A ∪ B is {1 to 8}, containing 8 elements, and the universal set has 10 elements. The elements outside the union are 9 and 10, so the complement is {9, 10}.

  1. A3
  2. B2Correct
  3. C4
  4. D1

Explanation

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}, which has 8 elements. Its complement in U is {9, 10}, which has 2 elements. Choosing 4 would come from computing the complement of A only partly, and 3 from wrongly using A′ ∩ B′ with a miscount.

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