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Let \(A = \{x \in \mathbb{N}|1 < x < 4\}\), \(B = \{x \in \mathbb{W}|0 \leq x < 2\}\) and \(C = \{x \in \mathbb{N}|x < 3\}\). Then verify 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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