Question

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

• A. $400$
• B. $240$
• C. $300$
• D. $500$

Answer 1

Answer: (C)

$300$

$n(A\cup B)=nA+nB-n(A\cap B)$

$=200+300-100$

$=400$

Hence $n(A\cup B)=400$ ...(i)

And

$n(A^{\prime }\cap B^{\prime })$

$=n(A\cup B{)}^{\prime }$

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

Therefore

$n\left(U\right)-n(A\cup B)$

$=700-400$ from ... (i)

$=300$