Ononot — Let S = \{1, 2, 3, 4, 5, 6, 7, 8\}. Consider a subset A \sub

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Set Theoryhard

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Let $S = \{1, 2, 3, 4, 5, 6, 7, 8\}$ . Consider a subset $A \subseteq S$ . We define two properties for $A$ : Property $P_1$ : $A$ contains at least one prime number. Property $P_2$ : The sum of the elements in $A$ is an even number. How many non-empty subsets $A \subseteq S$ satisfy both Property $P_1$ and Property $P_2$ ?