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 :

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 2 ^ 50 ( 2 ^ 50 - 1)

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

$= {2}^{100} - {2}^{50} = {2}^{50}\left({2}^{50} - 1\right)$ .

Let S = \ 1, 2, 3, . , 100\ , then number of non-empty subsets A of...