Question

Two finite sets have $m$ and $n$ number of elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. Then $m$ and $n$ are

• A. $7,6$
• B. $6,3$
• C. $5,1$
• D. $8,7$

Answer 1

The correct option is B $6,3$

Let $m>n$
Then $2^m=56+2^n$
$\Rightarrow 2^m-2^n=56$
$\Rightarrow 2^n(2^{m-n}-1)=2^3\times 7$
Comparing both sides, we get
$n=3$ and $2^{m-n}-1=7$
$\Rightarrow m=6,n=3$