Two finite sets have m and n elements.
Question:

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then, the values of m and n are:

(a) 7, 6

(b) 6, 3

(c) 7, 4

(d) 3, 7

Solution:

(c) 6, 4

ATQ :

$2^{m}-1=48+2^{n}-1$

$\Rightarrow 2^{m}-2^{n}=48$

$\Rightarrow 2^{m}-2^{n}=2^{6}-2^{4}$

By comparing we get:

$m=6$ and $n=4$