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Show that $A \times (B \cap C) = (A \times B) \cap (A \times C)$
written 9.0 years ago by gravatar for teamques10 teamques10 ★ 70k modified 3.9 years ago by gravatar for krithikkm200 krithikkm200 • 10

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 4 Marks

Year: May 2014
discrete mathematics
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written 9.0 years ago by gravatar for teamques10 teamques10 ★ 70k

Let (a, b) be an arbitrary element of A x (B Ո C). Then

(a, b) € A x (B Ո C)

-> a € A and b € (B Ո C)

-> a € A and (b € B and b € C)

-> (a € A and b € B) and (a € A and b € C)

-> (a, b) € (A X B) and (a, b) € (A X C)

-> (a, b) € (A X B) Ո (A X C)

Hence, A x (B Ո C) = (A x B) Ո (A x C)
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