Let $ S=\{1,2,3, \ldots, 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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Let \( S=\{1,2,3, \ldots, 100\} \). The number of non-empty subsets \( A \) of \( S \) such that the product of elements…