Question

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A\times B$ and $B\times A$ are

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

Answer 1

Answer: (B)

Here, given that $n\left(\right.A\cap B\left.\right)=99$
Now, $\left(\right.A\times B\left.\right)\cap \left(\right.B\times A\left.\right)=n\left(\right.A\cap B\left.\right)\times \left(\right.B\cap A\left.\right)$
$=n\left(\right.A\cap B\left.\right)\cdot n\left(\right.B\cap A\left.\right)$
$=n\left(\right.A\cap B\left.\right)\cdot n\left(\right.A\cap B\left.\right)$
$=99\cdot 99=99^{2}$