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.
Answer variants:
\(\{0,1,2\}\)
\(\{(2,0), (2,1), (3,0), (3,1)\}\)
\(\{(2,0), (2,1), (2,2), (3,0), (3,1), (3,2)\}\)
\(\{(2,1), (2,2), (3,1), (3,2)\}\)