Question

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

(1) 2⁵⁰ + 1 

(2) 2⁵⁰ (2⁵⁰ – 1) 

(3) 2¹⁰⁰ – 1 

(4) 2⁵⁰ – 1

Answer 1

The correct option (2) 2⁵⁰(2⁵⁰ – 1)

Explanation:

Product of elements in A is even = (total subjects) – (Number of subject of all whose element are odd) 

= 2¹⁰⁰ – 2⁵⁰

= 2⁵⁰(2⁵⁰ – 1)