Let S = 1 , 2 , 3 , … . , 100 , then number of non-empty subsets A of S such that the product of elements in A is even is :

Step-by-step solution

As we know that the product of numbers is even when at least one of the number must be even. Hence total subsets of A in which product of numbers is even = Total subsets – total subsets in which all the elements are odd = 2 100 - 2 50 = 2 50 2 50 - 1 .