Question:
If $P$ and $Q$ are two sets such that $P$ has 40 elements, $P \cup Q$ has 60 elements and $P \cap Q$ has 10 elements, how many elements does $Q$ have?
Solution:
Given:
$n(P)=40$
$n(P \cup Q)=60$
$n(P \cap Q)=10$
To find :
$n(Q)$
We know :
$n(P \cup Q)=n(P)+n(Q)-n(P \cap Q)$
$\Rightarrow 60=40+n(Q)-10$
$\Rightarrow n(Q)=30$
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