If $n (A) = 5, n (B) = 7$ be two sets having $3$ elements in common then $n ((A \times B) \cap (B \times A)) =$

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Solution

As we know that
$(A \times B) \cap (B \times A) = (A \cap B) \times (B \cap A)$
So $n ((A \cap B) \times (B \cap A)) = n (A \cap B) \times n (B \cap A)$
$= 3 \times 3 = 9$

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