Complement of a Set

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New answer posted•a year ago

If n(A U B U C) + n((A U B U C)') = 50, n(A)=10, n(B)=15, n(C)=20, n(A∩B)=5, n(B∩C)=6, n(C∩A)=10, n(A∩B∩C)=5, then the value of n(A U B U C)'

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a year ago

$n (A \cup B \cup C) + n (A \cup B \cup C)^{'} = 50$

$n (\cup) = 50$

$n (A \cup B \cup C)^{'} = n (\cup) - n (A \cup B \cup C) \Rightarrow 50 - 29 \Rightarrow 21$

$n (A \cup B \cup C) = n (A) + n (B) + n (C) - n (A \cap B) - n (B \cap C) - n (C \cap A) - n (A \cap B \cap C)$

$\Rightarrow 10 + 15 + 20 - 5 - 6 - 10 - 5 \Rightarrow 29$

$n (A \cup B \cup C)^{'} = 21$

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