Question

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

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

Answer 1

The correct option is B $6,3$

$\because$ The number of subsets of a set containing $p$ elements = $2^p$
Here, $2^m-2^n=56$
The values of n and n satisfying the given equations form the given option are $6,3$.
$2^6-2^3=64-8=56.$