Question

A and B are two sets having $3$ elements in common.If $n\left(A\right)=5,n\left(B\right)=4$ then Find $n\left(A\times B\right)andn\left[\left(A\times B\right)\cap \left(B\times A\right)\right]$

Answer 1

Consider the problem

The elements in the order pair

$\begin{array}{c}A\times B=5\times 4=20\\ n\left(A\times B\right)=20\end{array}$

Since, three elements are common in the set $A$ and $B$

Therefore, the number of common elements in the order pair set is

$\begin{array}{c}3\times 3=9\\ n\left[\left(A\times B\right)\cap \left(B\times A\right)\right]=9\end{array}$