Two finite sets have `m` and `n ( m gt n)` elements .The number of sube of the first set is `112` more than that of the second set. The value of `mn` is

Options

A. 18
B. 28
C. 32
D. 36

Answer

B

Explanation

According to the question
`2^m-2^m= 112 `
`rArr 2^n (2^(m-n)-1)= 2^4 xx 7`
Comparing exponets on both sides ,we get
`2^n-2^4 and 2^(m-n)-1= 7 `
Now ,`2^n= 2^4`
`rArr n=4`
And `2^(m-n)=8`
`rArr 2^(m-n)=2^3`
`rArr m-n =3`
`therefore m=7`