Question

If the difference between the number of subsets of the sets $A$ and $B$ is $120$ , then choose the incorrect option.

• A. Maximum value of $n\left(A \cap B\right)=3$
• B. Minimum value of $n\left(A \cap B\right)=0$
• C. Maximum value of $n\left(A \cup B\right)=21$
• D. Minimum value of $n\left(A \cup B\right)=7$

Answer 1

Answer: (C)

Let, $n\left(A\right)=\alpha ,n\left(B\right)=\beta \left(\alpha > \beta \right)$
given, $2^{\alpha }-2^{\beta }=120\Rightarrow \alpha =7,\beta =3$
$\therefore n\left(A \cap B\right)\in \left[0 , 3\right]\because n\left(A \cup B\right)=\alpha +\beta =n\left(A \cap B\right)$
$n\left(A \cup B\right)\in \left[7 , 10\right]$