PDF chapter test TRY NOW
Verify \(n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)\) for the sets \(A = \{a, c, e, f, h\}\), \(B = \{c, d, e, f\}\) and \(C = \{a, b, c, f\}\).
Proof:
\(n(A \cup B \cup C) =\) ---- (\(1\))
\(n(A) =\)
\(n(B) =\)
\(n(C) =\)
\(n(A \cap B) =\)
\(n(B \cap C) =\)
\(n(A \cap C) =\)
\(n(A \cap B \cap C) =\)
\(n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C) =\) ---- (\(2\))
From equations (\(1\)) and (\(2\)), we have: \(n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)\).
Hence, we proved.