Question

If $A$ and $B$ are two sets and $U$ is the universal set such that $n\left(U\right)=700,n\left(A\right)=200,n\left(B\right)=300$ and $n(A\cap B)=100$, find $n(A^{\prime }\cap B^{\prime })$.

Answer 1

We need to find $n(A^{\prime }\cap B^{\prime })$

$n(A^{\prime }\cap B^{\prime })=n\left(U\right)-n(A\cup B)$ ....(i)

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

$n(A\cup B)=400$

Put in equation (i), we get

$n(A^{\prime }\cap B^{\prime })$$=700-400=300$