Question

Two finite sets have m and n elements. The number of elements in the power set of first is 48 more then the total number of elements in power set of the second set. Find m&n.

Answer 1

Power set of set $1$ is, P(set $1$)$=2^m$

Power set of set $2$ is, P(set $2$)$=2^n$

By given condition,

$2^m=48+2^n$

$\therefore 2^m-2^n=48$

$\therefore 2^m-2^n=64-16$

$\therefore 2^m-2^n=2^6-2^4$

$\therefore m=6$ and $n=4$.