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Two finite set have m and n elements.the total number of subsets of first set is 56 more than total number of subset of second set. find the values of m and n?

Let A denote the first set and B denote the second.
We have n(A) = 2m and B(A) = 2n
We have n(A) = 56 + n(B)
n(A) - n(B) = 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 = 2 6 -3
n = 3 or m - n = 3
n = 3 or m = 6
Hence m = 6 and n = 3


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