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 ?

Answer 1

We have, $n\left(P\right)=40,n(P\cup Q)=60,n(P\cap Q)=10,$to find n(Q).

We know $n(P\cup Q)=n\left(P\right)+n\left(Q\right)-n(P\cap Q)$

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

$\Rightarrow 60=30+n\left(Q\right)$

$\Rightarrow n\left(Q\right)$= 60- 30

= 30

Hence, Q has 30 elements.