Let n(A) = m and n(B) = n, if the number of subsets of A is 56 more than of subsets of B, then m + n is equal to

Since, total possible subsets of sets A and B are 2m and 2n, respectively.According to given condition,2m−2n=56⇒2n2m−n−1=23×23−1On comparing both sides, we get2n=23 and 2m−n=23⇒n=3 and m−n=3⇒m=6 and n=3Now, m + n =6+3=9