Question

Two finite sets have $m$ and $n$ elements. If the number of subsets of the first set is $112$ more than the number of subsets of the second set, then find the value of $m\times n$.

Answer 1

Let the first set $=A$

number of subset$=2^m$

Let the second set be=$B$

number of subset$=2^n$

$\because 2^m-2^n=1122^n(2^{m-n}-1)=128-162^n(2^{m-n}-1)=2^4(2^3-1)Equaten=4m-n=3m=n+3m=4+3=7\therefore m\times n=4\times 7=28$