Question

If $n\left(A\right)=26,n\left(B\right)=10,n(A\cup B)=30,n\left(A^{\prime }\right)=17$, find $n(A\cap B)$ and $n(\cup )$.

Answer 1

$n\left(A\right)=26,n\left(B\right)=10,n(A\cup B)=30,n\left(A^{\prime }\right)=17$

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

$30=26+17-n(A\cap B)$

$30=43-n(A\cap B)$

$n(A\cap B)=43-30$

$n(A\cap B)=13$

We are given $n\left(A^{\prime }\right)=17$

or, $17=n\left(U\right)-n\left(A\right)$

or, $n\left(U\right)=17+26$ [Since $n\left(A\right)=26$]

or, $n\left(U\right)=43$.