Question

If two sets $A$ and $B$ are having $43$elements in common, then the number of elements common to each of the sets$A\times B$and $B\times A$is

• A. ${43}^2$
• B. $2^{43}$
• C. ${43}^{43}$
• D. $2^{86}$

Answer 1

The correct option is A

${43}^2$

Explanation for the correct answer:

Find the number of elements common to each of the sets $A\times B$and $B\times A$:

We know,

$\begin{array}{rcl}n\left(\right(AxB)\cap (BxA\left)\right)& =& n\left(\right(A\cap B)x(B\cap A\left)\right)\\ & =& n(A\cap B).n(B\cap A)\\ & =& 43x43\left[\mathrm{given}\right]\\ & =& {43}^2\end{array}$

Hence, the correct option is (A).