Question

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

Answer 1

Again... the first hit of your exact question gave a well layed out explanation....
It went like this.
Let M and N be two sets having m and n numbers of elements. The number of subsets of M = 2m and the number of subsets of N =2n.
The question stated that they subsets differ by 56. Written mathematically that is, 2m - 2n = 56
...

Answer 2

Since the number of subsets of k elements is 2^k ,
I think you mean
2^m - 2^n = 56
by inspection, the powers of 2 are
1, 2, 4, 8, 16, 32, 64, 128, 256, ....
so we want a difference of two of these of 56
No need to go higher than 64 ...
64 - 16 = 48, not what we want
64 - 8 = 56 , THAT'S THE ONE

3^6 - 2^3 = 56
so m = 6 and n = 3