Question

Two finite sets have $m$ and $n$ elements, then total number of subsets of the first set is $56$ more that the total number of subsets of the second. The value of $m$ and $n$ are,

• A. $7,6$
• B. $6,3$
• C. $5,1$
• D. $8,7$

Answer 1

Answer: (B)

$6,3$

Since the two finite sets have $m$ and $n$ elements,

So number of subsets of these sets will be $2^m$ and $2^n$ respectively.

According to the question $2^m-2^n=56$

Putting $m=6,n=3$ we get

$2^6-2^3=56\Rightarrow 64-8=56$