Let S = (1, 2, 3, ... , 50). The number of non-empty subsets A of S such that product of element in A is even, is  2m2n−1 then the value of (m + n) is equal to

Given, Set S = {1,2,3, ... 50}.Total number of non-empty subset of  'S′=250−1Now, number of non-empty subset of  S in which onlyodd number. {1,3,5,... 49} occurs =225−1So, the required number of non-empty subsets of  S,such that product of elements is even.250−1−225−1=250−1−225+1=250−225=225225−1Here, m=n=25∵m+n=25+25=50