Ononot — Let S = \{1, 2, 3\}. Let \mathcal{P}(S) denote the power set

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Set Theoryhard

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Let $S = \{1, 2, 3\}$ . Let $\mathcal{P}(S)$ denote the power set of $S$ . Consider the set $X = \{ A \in \mathcal{P}(S) : |A| \text{ is even} \}$ . Consider the set $Y = \{ A \in \mathcal{P}(S) : 1 \in A \}$ . Find the cardinality of the set $X \cap Y$ .