Question

Two finite sets have m and n elements. The total number of subsets of the first set is $48$ more than the total number of subsets of the second set. The values of m and n are?

• A. $7,6$
• B. $6,7$
• C. $6,4$
• D. $7,4$

Answer 1

Answer: (C)

$6,4$

No of subset for the $1^{st}$set = $2^m$

No of subset for the $2^{nd}$ set = $2^n$

Atp,

$2^m-2^n=48$

$2^n(2^{m-n}-1)=16\times 3$

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

Comparing them, we get

$n=4,m-n=2$

$n=4,m=6$