Question

If $n(\cup )=900$, $n\left(A\right)=300$, $n\left(B\right)=200$, $n(A\cap B)=100$, then find $n(A^{{}^{\prime }}\cap B^{{}^{\prime }})$.

Answer 1

GIven, $n(\cup )$= 900, $n\left(A\right)=300$, $n\left(B\right)=200$ , $n(A\cap B)=100$

We know that,
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$n(A\cup B)=300+200-100$
$n(A\cup B)=400$

Now,
$n(A^{{}^{\prime }}\cap B^{{}^{\prime }}$) = $n\left(U\right)-n(A\cup B)$
$n(A^{{}^{\prime }}\cap B^{{}^{\prime }}$) = $900-400=500$