Question

If $n(\cup )=38,n\left(A\right)=16,n(A\cap B)=12,n\left(B^{\prime }\right)=20$, find $n(A\cup B)$.

Answer 1

$n\left(V\right)=38,n\left(A\right)=16,n(A\cap B)=12,n\left(B^{\prime }\right)=20$

$n\left(B\right)=n\left(U\right)-n\left(B^{\prime }\right)$

$=38-20$

$=18$

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

$n(A\cup B)=16+18-12$

$n(A\cup B)=22$