Question

If two sets $A$ and $B$ are having $99$ elements in common, then the number of ordered pairs common to each of the sets $AxB$ and $BxA$ are

• A. $2^{99}$
• B. ${99}^2$
• C. $100$
• D. $18$

Answer 1

The correct option is B ${99}^2$

Let us the $n\left(\left(A\times B\right)\cap \left(B\times A\right)\right)$

$=n\left(\left(A\cap B\right)\times \left(B\cap A\right)\right)$

$=n\left(A\cap B\right).n\left(B\cap A\right)$

$=n\left(A\cap B\right).n\left(A\cap B\right)$

$=\left(99\right)\left(99\right)$

$={99}^2$