Let S = {1, 2, 3, dots, 100}. The number of n | vedclass

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(C) The product of elements in a subset $A$ is even if at least one element in the subset is even.Total number of non-empty subsets of $S$ is $2^{100}

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$2^{100} - 2^{50}$

Vedclass · Answer

(C) The product of elements in a subset $A$ is even if at least one element in the subset is even.Total number of non-empty subsets of $S$ is $2^{100} - 1$.The number of subsets containing only odd elements is $2^{50} - 1$ (since there are $50$ odd numbers in the set $S = \{1, 2, \dots, 100\}$).Therefore,the number of subsets where the product is even is the total number of non-empty subsets minus the number of subsets containing only odd elements.Number of subsets = $(2^{100} - 1) - (2^{50} - 1) = 2^{100} - 2^{50}$.

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

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