Question

Two finite sets have $m$ and $n$ elements respectively. The total number of subset of the first set is $56$ more than the total no. of subsets of the second set.The values of $m$ and $n$ respectively will be

• A. $m=3,n=3$
• B. $m=6,n=3$
• C. $m=3,n=6$
• D. None of these

Answer 1

The correct option is B $m=6,n=3$

Let $A$ and $B$ be two sets having $m$ and $n$ numbers of elements respectively

number of subsets of $A=2^m$

number of subsets of $B=2^n$

according to question

$2^m-2^n=56$

$2^n(2^{m-n}-1)=23(2^3-1)$

$\therefore ,n=3$ and $m-n=3$

$m=6$