Question

Two infinite 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.
A. 4,7
B. 7,4
C. 4,4
D. 7,7

Answer 1

Correct Answer - A
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`