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 :

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) 250 (250 - 1) (B)  2100 - 1  (C)  250 - 1  (D)  250 + 1

Tardigrade Admin · Accepted Answer

S = 1,2,3------100 = Total non empty subsets-subsets with product of element is odd = 2100 - 1 - 1[(250 - 1)] = 2100 - 250 = 250 (250 - 1)

Q. 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 :

$2^{50} (2^{50} - 1)$

$2^{100} - 1$

$2^{50} - 1$

$2^{50} + 1$

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

Q. 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 :

250(250−1)

2100−1

250−1

250+1