Let \(A = \{x \in \mathbb{N}|\)\(2 \leq x \leq 3\}\), \(B = \{x \in \mathbb{W}|\)\(0 \leq x \leq 1\}\) and \(C = \{x \in \mathbb{N}|\)\(x \leq 2\}\). Then establish that \(A \times (B \cup C) = (A \times B) \cup (A \times C)\)
Answer:
To prove:
\(A \times (B \cup C) = (A \times B) \cup (A \times C)\)
Explanation:
\(B \cup C =\)
\(A \times (B \cup C) =\)
\(A \times B =\)
\(A \times C =\)
\((A \times B) \cup (A \times C) =\)
As a result, \(A \times (B \cup C) = (A \times B) \cup (A \times C)\)
Hence, we proved.
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