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Show that $A-(B-C)=(A-B) \cup ( A \cap B \cap C)$
written 8.0 years ago by gravatar for teamques10 teamques10 ★ 68k modified 2.9 years ago by gravatar for pedsangini276 pedsangini276 • 4.8k

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 4 Marks

Year: May 2015
discrete mathematics
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written 8.0 years ago by gravatar for teamques10 teamques10 ★ 68k

Let (a, b) be an arbitrar y element of A-(B-C). Then

(a, b) € A-(B-C)

-> a € A and b € (B - C)

-> a € A and (b € B and b € C)

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

-> (a, b) € (A - B) and (a, b) € (AՈBՈC)

-> (a, b) € (A - B) U (AՈBՈC)

Hence, A-(B-C)=(A-B)U( AՈBՈC)
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