Let \(X = \{x \in \mathbb{N}|1 < x < 4\}\), \(Y = \{x \in \mathbb{W}|0 \leq x < 2\}\) and \(Z = \{x \in \mathbb{N}|x < 3\}\). Then demonstrate that \(X \times (Y \cap Z) = (X \times Y) \cap (X \times Z)\)
Answer:
To prove:
\(X \times (Y \cap Z) = (X \times Y) \cap (X \times Z)\)
Explanation:
\(Y \cap Z = \{\)\(\}\)
\(X \times (Y \cap Z) = \{\)\(\}\)
\(X \times Y = \{\)\(\}\)
\(X \times Z = \{\)\(\}\)
\((X \times Y) \cap (X \times Z) =\{\)\(\}\)
As a result, \(X \times (Y \cap Z) = (X \times Y) \cap (X \times Z)\)
Hence, we proved.