If P and Q are two sets such that P has 40 elements,
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 :

$n(P \cup Q)=n(P)+n(Q)-n(P \cap Q)$

$\Rightarrow 60=40+n(Q)-10$

$\Rightarrow n(Q)=30$