Set Theoryhard
0:00.0
Let . For any subset , let denote the sum of its elements (with ). Let us define two collections of subsets:
$$\mathcal{A} = \left{ A \in P(S) : f(A) \text{ is even} \right}$
\mathcal{B} = \left\{ B \in P(S) : |B \cap \{1, 2, 3, 4\}| \ge 3 \right\}$$
Determine the cardinality of the intersection \mathcal{A} \cap \mathcal{B}$.
Let . For any subset , let denote the sum of its elements (with ). Let us define two collections of subsets: $$\mathcal{A} = \left{ A \in P(S) : f(A) \text{ is even} \right}$
\mathcal{B} = \left\{ B \in P(S) : |B \cap \{1, 2, 3, 4\}| \ge 3 \right\}$$ Determine the cardinality of the intersection \mathcal{A} \cap \mathcal{B}$.