1. Problem: Find $n[(A \times B) \cup (A \times C)]$ given $n(A) = 2$ and $n(B \cup C) = 3$.
2. Formula: For sets $A$, $B$, and $C$, the Cartesian product $A \times (B \cup C) = (A \times B) \cup (A \times C)$.
3. Using the formula, $n[(A \times B) \cup (A \times C)] = n[A \times (B \cup C)] = n(A) \times n(B \cup C)$.
4. Substitute values: $n(A) = 2$, $n(B \cup C) = 3$.
5. Calculate: $2 \times 3 = 6$.
6. Final answer: $6$.
Cartesian Union De6201
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