Question

two infinite sets have m and n elements. the total number of subsets of the first set is 56 more than total number of subsets of the second set. find the value of m and n.

Answer 1

Let x denote the first set and y denote the second set.
We have, n(x) = 2m
and n(y) = 2n.
As per the question, we have
n(x) = 56 + n(y)
n(x) - n(y) = 56
2m - 2n = 56
2n (2m-n - 1)
2n (2m-n - 1) = 8 × 7
2n = 8 = 23 or (2m-n - 1) = 7
n = 3 or 2m-n = 8 = 23 = 26-3
n = 3 or m - n = 3
n=3 or m=6
required values of m and n are 6 and 3.
hope this will help...