Question

Let $n\left(\right.A\left.\right)$ 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 $n\left[\right.\left(\right.A\times B\left.\right)\cap \left(\right.B\times A\left.\right)\left]\right.$ 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 $n\left(A \cap B\right)=3$
$\therefore n\left[\left(A \times B\right) \cap \left(B \times A\right)\right]=n\left[\left(A \cap B\right) \times \left(B \cap A\right)\right]=3^{2}=9$