Two finite sets have `m` and `n` elements. The number of subsets of the first set is `112` more than that of the second set. The values of `m` and `n` are, respectively.

Options

A. `4, 7`
B. `7,4`
C. `4,4`
D. `7,7`

Answer

B

Explanation

Since, number of subsets of a set containing m elements is 112 more than the subsets of the set containing n elements.
`:. 2^(m) - n^(n) = 112`
`rArr 2^(n). (2^(m-n) - 1) = 2^(4).7`
`rArr 2^(n) = 2^(4)` and `2^(m-n) - 1 = 7`
`rArr n = 4` and `2^(m-n) = 8`
`rArr 2^(m-n) = 2^(3) rArr m - n = 3`
`rArr m - 4 = 3 rArr m = 4 + 3`
`:. m = 7`