Question

If sets $A$ and $B$ are not disjoint, then $n(A\cup B)$ is equal to

• A. $n\left(A\right)+n\left(B\right)$
• B. $n\left(A\right)+n\left(B\right)-n(A\cap B)$
• C. $n\left(A\right)+n\left(B\right)+n(A\cap B)$
• D. $n\left(A\right)$, $n\left(B\right)$

Answer 1

Answer: (B)

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

In all cases(even if sets A and B are disjoint)

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$, only that $n(A\cap B)=0$ if they are disjoint.