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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

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a

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

b

$2^{50} + 1$

c

$2^{100} - 1$

d

$2^{50} - 1$

answer is B.

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Detailed Solution

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Total of subsets $= 2^{100} - 1$
No.of subsets without even number $= 2^{50} - 1$
Required number of subsets $= 2^{100} - 2^{50}$

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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