Question

If $A$ and $B$ are two disjoint sets, then the relation between them is

• A. $n(A\cup B)=n\left(A\right)+n\left(B\right)$
• B. $n\left(A\right)+n\left(B\right)=n(A\cup B)+n\left(AIB\right)$
• C. $n(A\cup B)=n\left(AIB\right)$
• D. $n\left(AIB\right)=n\left(A\right)+n\left(B\right)$

Answer 1

The correct option is A $n(A\cup B)=n\left(A\right)+n\left(B\right)$

$A$ and $B$ are two disjoint sets.

$\therefore$ $A\cap B=\varphi$ $⟹$ $n(A\cap B)=0$

Since, $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$=n\left(A\right)+n\left(B\right)-0=n\left(A\right)+n\left(B\right)$

Hence, $n(A\cup B)=n\left(A\right)+n\left(B\right)$