Ononot — Let A and B be two sets. We define the set S = P(A \cup B) \

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Set Theoryhard

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Let $A$ and $B$ be two sets. We define the set $S = P(A \cup B) \setminus (P(A) \cup P(B))$ , where $P(X)$ denotes the power set of $X$ . If $|A| = 4$ , $|B| = 5$ , and $|A \cap B| = 2$ , find the cardinality of the set $S$ .