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Set Theoryhard
0:00.0

Let S={1,2,3,4}S = \{1, 2, 3, 4\}S={1,2,3,4}. Consider the set A={A⊆S:1∈A and A∩{2,3}≠∅}\mathcal{A} = \{A \subseteq S : 1 \in A \text{ and } A \cap \{2, 3\} \ne \emptyset\}A={A⊆S:1∈A and A∩{2,3}=∅}. Determine the cardinality of A\mathcal{A}A.