Question

Let $n(A)=m$ and $n(B)=n$, if the number of subsets of $A$ is $56$ more than of subsets of $B$, then $m+n$ is equal to

• A. 9
• B. 13
• C. 8
• D. 10

Answer 1

Answer: (A)

Since, total possible subsets of sets $A$ and $B$ are $2^{m}$ and $2^{n}$, respectively.
According to given condition,
$2^{m}-2^{n} =56$
$\Rightarrow 2^{n}\left(2^{m-n}-1\right) =2^{3} \times\left(2^{3}-1\right)$
On comparing both sides, we get
$2^{n} =2^{3}$ and $2^{m-n}=2^{3}$
$\Rightarrow n=3$ and $m-n=3$
$\Rightarrow m=6$ and $n=3$
Now, $m+n=6+3=9$