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KCET2012MathematicsSets and Relations

If A and B have n elements in common, then the number of elements common to A B and B A is

Options

  1. An
  2. B2 n
  3. Cn ²
  4. D0

Correct answer

C. n ²

Step-by-step solution

Let C = A B , then C C=(A B) (A B)=(A B) (B A) gathered =(A B) (B A) [ (A C) (B D)=(A B) (C D)] gathered Since, A B has n elements, so C has n elements. Hence, C C has n ² elements. ( A B ) ( B A ) has n ² elements. Hence, A B and B A has n ² elements in common.

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