Question

If the difference between the number of subsets of two sets $A$ and $B$ is $120$ , then $n\left(A\times B\right)$ is equal to

• A. $21$
• B. $25$
• C. $18$
• D. $24$

Answer 1

Answer: (A)

Let, $n\left(A\right)=\alpha \&n\left(B\right)=\beta$
Given, $\left|2^{\alpha }-2^{\beta }\right|=120\Rightarrow \left(\alpha ,\beta \right)\equiv \left(7,3\right),\left(3,7\right)$
$\therefore n(A\times B)=7\times 3=21$