Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than the total no. of subsets in the second set. Find the value of m and n.

If some set A has n elements, then it has 2^n subsets.

Using that, the sentence, "The total number of subsets of ‘m’ is 56 more than the total number of subsets of ‘n’." gives you the equation 2^m - 2^n = 56

Factor both sides: 2^n * (2^ (m-n) - 1) = 2^3 * 7

Since 2^n is a power of 2 and (2^ (m-n) - 1) is an odd integer, we must have 2^n = 2^3 2^ (m-n) - 1 = 7

Solving these, you get n = 3 and m = 6.