• # question_answer Let A = {1, 2, 3, 4, 5}; B = {2, 3, 6, 7}. Then the number of elements in $\left( A\text{ }~\times \text{ }B \right)\text{ }\cap \text{ }\left( B\text{ }\times \text{ }A \right)$ is A) 18 B) 6 C) 4 D) 0

Here A and B sets having 2 elements in common, so $A\times B$ and $B\times A$ have ${{2}^{2}}$ i.e., 4 elements in common. Hence, $n\,[(A\times B)\cap (B\times A)]=4$.