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 :

• A. $2^{50} (2^{50} - 1)$
• B. $ 2^{100} - 1 $
• C. $ 2^{50} - 1 $
• D. $ 2^{50} + 1 $

Answer 1

Answer: (A)

S = {1,2,3------100}
= Total non empty subsets-subsets with product of element is odd
$= 2^{100} - 1 - 1[(2^{50} - 1)]$
$= 2^{100} - 2^{50}$
$= 2^{50} (2^{50} - 1)$