Question

If A and B are two sets such that $n(A\cup B)$ = 50, n(A) = 28 and n(B) = 32, find $n(A\cap B)$.

Answer 1

$n(A\cup B)$ = 50, n(A)= 28, n(B)= 32, where n(x) does notes the cardinal number of the set x.

We know that $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow 50=28+32-n(A\cap B)$

$\Rightarrow 50=60-n(A\cap B)$

$\Rightarrow n(A\cap B)=60-50=10$

$\therefore n(A\cap B)=10$