Question

Let $A$ and $B$ are two sets having 3 elements in common. If $n(A)=5$ and $n(B)=4$, then $n[(A\times B)\cap (B\times A)]$ is equal to

• A. 20
• B. 25
• C. 16
• D. 9

Answer 1

Answer: (D)

Given, $n(A)=5,n(B)=4,n(A\cap B)=3$
$n[(A\times B)\cap (B\times A)]$
$=n[(A\cap B)\times (B\cap A)]$
$=n(A\cap B)\times n(B\cap A)[\because n(A\cap B)=n(B\cap A)]$
$=3\times 3=9$