Question

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

• A. $7,6$
• B. $6,3$
• C. $6,4$
• D. $7,4$

Answer 1

Answer: (C)

$6,4$

Solution :-

Given two finite sets have $m$ and $n$ element

Number of element in the power set of first set

is $48$ more than the total number of elements

is power set of the second set.

i.e., $2^m-2^n=48$

We have $1$ equation in $2$ unknowns,

Therefore infinitely many solutions exist.

But the only integer solution is $m=6$ and $n=4$.