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  2. Question
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  4. A, B, C are three sets such that n(A)=25, n(B)=20, n(c)=27, n(A ∩ B)=5, n(B ∩ C)=7 and A ∩ C= φ then n(A ∪ B ∪ C) is equal to

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Q. $A, B, C$ are three sets such that $n(A)=25$, $n(B)=20, n(c)=27, n(A \cap B)=5, n(B \cap C)=7$ and $A \cap C=$ $\phi$ then $n(A \cup B \cup C)$ is equal to

Sets

Solution:

$A \cap C=\phi $
$\Rightarrow A \cap B \cap C=\phi$.
$\therefore 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) $
$= 25+20+27-5-7-0+0=60 .$