If n(A) = 50, n(B) = 48, n(C) = 42, n(AnB) = 12, n(BnC)=8, n(CnA)=9, j(AnBnC)=5 and n(U)=125, find the value of n(AuBuC) and n(AuBuC)^c.

Solution:

Given,

$n(U) = 125$

$n(A) = 50$

$n(B) = 48$

$n(C) = 42$

$n(A \cap B) = 12$

$n(B \cap C) = 8$

$n(A \cap C) = 9$

$n(A \cap B \cap C) = 5$

To find:

$n(A \cup B \cup C) = ?$

$n(\overline{ A\cup B \cup C}) = ?$

Using formula,

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

$= 50 + 48 + 42 - \{ 12 + 8 + 9 \} + 5$

$= 116$

Also,

$n( \overline {A \cup B \cup C}) = n(U) - n(A \cup B \cup C)$

$= 125 - 116$

$= 9$

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