For any sets \( A, B \) and \( C \), prove that: (i) \( A \times(B \cup C)=(A \times B) \cup(A \...

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For any sets \( A, B \) and \( C \), prove that:
(i) \( A \times(B \cup C)=(A \times B) \cup(A \times C) \)
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