Question

If $n(\cup )=700$, $n\left(A\right)=200$, $n\left(B\right)=300$ , $n(A\cap B)=100$, then $n(A^{{}^{\prime }}\cap B^{{}^{\prime }})$

• A. 400
• B. 240
• C. 300
• D. 500

Answer 1

The correct option is C

300

GIven, $n(\cup )$= 700, $n\left(A\right)=200$, $n\left(B\right)=300$ , $n(A\cap B)=100$

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

Now,
$n(A^{{}^{\prime }}\cap B^{{}^{\prime }}$) = $n\left(U\right)-n(A\cup B)$
$n(A^{{}^{\prime }}\cap B^{{}^{\prime }}$) = $700-400=300$