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. Find the values of m and n.

Answer 1

Solution:

Let A and B are two sets having elements $m$ and $n$.

Number of subsets of set $A=2^m$

Number of subsets of set $B=2^n$

$2^m-2^n=56$

$2^n\left(2^m/2^n\right)-1=7\times 8$

$2^n\times 2^{(m-n)}-1=2^3+(2^{(4–1)}-1)$

On comparing we can get

$m=4$

$n=3$