Question

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

• A. $2,4$
• B. $6,3$
• C. $3,6$
• D. $4,2$

Answer 1

The correct option is B $6,3$

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

Number of subsets of $A=2^m$ and the number of subsets of $B=2^n$

It is given that, $2^m-2^n=56$

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

or, $n=3$ and $m-n=3\Rightarrow m=6$