Question

Let $U$ be a Universal set and $n(U)=12$. If $A,B\subseteq U$ are such that $n(B)=6$ and $n(A\cap B)=2$ then $n\left(A\cup B^{\prime }\right)$ is equal to

• A. 6
• B. 10
• C. 7
• D. 8

Answer 1

Answer: (D)

$n\left(A\cup B^{\prime }\right)=n(A)+n\left(B^{\prime }\right)-n\left(A\cap B^{\prime }\right)$
$=n(A)+n(U)-n(B)-(n(A)-n(A\cap B))$
$=n(U)-n(B)+n(A\cap B)$
$=12-6+2=8$