Question

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $64$ more than the total number of subsets of the second set. The values of $m$ and $n$ are

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

Answer 1

The correct option is A $m=7,n=6$

total numbers of subset of a set with $K$ element is equal to $2^K$

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

$\therefore m=7$ and $n=6$