Let S = {1, 2, 3, ….., 100} . number of non-empty subsets A of S such that product of element

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1.Set Theory

hard

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

$2^{100} -1$

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

$2^{50} -1$

$2^{50} + 1$

(JEE MAIN-2019)

Solution

Product is even when atleast one element of subset is even Hence required number of subsets = total subsets -number of subsets all whose elements are odd $= 2^{100} – 2^{50}$

Standard 11

Mathematics

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Solution

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