Question

Let $n(A)$ denotes the number of elements in the set $A$ . If $n\left(A\right)=4,n\left(B\right)=5$ and $n\left(A\cap B\right)=3$ , then $n[(A\times B)\cap (B\times A)]$ is equal to

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

Answer: (B)

Given, $n\left(A\right)=4,n\left(B\right)=5$ and $n\left(A\cap B\right)=3$
$\therefore n\left[\left(A\times B\right)\cap \left(B\times A\right)\right]=n\left[\left(A\cap B\right)\times \left(B\cap A\right)\right]=3^2=9$