Two finite sets have m and n elements respectively. the total no. of subset of the first set is 56 more than the total no. of subsets of the second set. the values of m and n respectively will be

Let A and B be two sets having m and n numbers of elements respectively

number of subsets of A=2^{m}

number of subsets of B=2^{n}

according to question

2^{m}-2^{n}=56

2^{n}(2^{m-n}-1)=2^{3}(2^{3}-1)

therefore,

n=3 and m-n=3

m=6