Question

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 .

Answer 1

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.