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Prove that:n( AUBUC) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩B) - n(B∩C) + n(A∩B∩C). |
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Answer» \(n((A \cup B) \cup C) = n(A\cup B) + n(C) - n((A \cup B)\cap C)\) \((\because n (A \cup B) = n(A + n(B) - n(A \cap B))\) \(= n(A) + n(B) - n(A \cap B) + n(C) - n((A \cap C) \cup(B \cap C))\) \(= n(A) + n(B) + n(C) - n(A \cap B) - (n(A\cup C) + n(B \cap C) - n(A \cap C) \cap (B \cap C))\) \(= n(A) + n(B) + n(C) - n(A \cap B) - n(A\cap C) - n(B \cap C) + n(A \cap B\cap C) \) Hence Proved. |
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