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A × (B union C) = (A × B) UNION ( A × C)\(A \times (B\cup C) = (A\times B)\cup (A\times C)\) |
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Answer» \(A \times (B\cup C) = (A\times B)\cup (A\times C)\) Let \((x, y) \in A\times (B \cup C)\) \(\Leftrightarrow x \in A \) and \(y \in (B\cup C)\) \(\Leftrightarrow x \in A \) and \(y \in B \;or\;y\in C\) \(\Leftrightarrow x \in A \) and \(y \in B \;or\;x\in A \;or\; y\in C\) \(\Leftrightarrow (x,y) \in A \times B \;or\; (x,y)\in (A \times C)\) \(\Leftrightarrow (x, y) \in (A \times B)\cup (A\times C)\) \(\therefore A \times (B \cup C) = (A \times B)\cup (A \times C)\) |
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