Question

If $AandB$ are disjoint sets, 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. $n\left(A\right)+n\left(B\right)+n(A+B)$
• E. $n\left(A\right)–n\left(B\right)$

Answer 1

The correct option is A

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

Explanation for the correct option:

Finding the value:

If$AandB$ are disjoint sets,

$$\begin{gathered} n(A\cap B)=0 \\ n(A\cup B)=n\left(A\right)+n\left(B\right)–n(A\cap B) \\ n(A\cup B)=n\left(A\right)+n\left(B\right) \end{gathered}$$

Hence, the correct answer is option (A).