Question

If $n\left(A\right)=20,n\left(B\right)=30$ and $n(A\cup B)=40$, then $n(A\cap B)$ is equal to:

• A. $50$
• B. $10$
• C. $40$
• D. $70$

Answer 1

Answer: (B)

$10$

We know that for any two finite sets $A$ and $B$, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$.

Here, it is given that $n\left(A\right)=20,n\left(B\right)=30$ and $n(A\cup B)=40$, therefore,

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)\Rightarrow 40=20+30-n(A\cap B)\Rightarrow 40=50-n(A\cap B)\Rightarrow n(A\cap B)=50-40\Rightarrow n(A\cap B)=10$

Hence, $n(A\cap B)=10$