Question

For any two sets $A\&B,n\left(A\right)=20;n\left(B\right)=6;$$n(A\cup B)=22,$ then match the following:

• A. $4$
• B. $2$
• C. $16$

Answer 1

Given two sets $A\&B$ such that:
$n\left(A\right)=20;n\left(B\right)=6;n(A\cup B)=22$

Now, In order to find $n(A-B)\text{and}n(B-A),$ we need to find the value of $n(A\cap B)$

Now, using the relation:
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$\Rightarrow n(A\cap B)=n\left(A\right)+n\left(B\right)-n(A\cup B)=20+6-22=4$

$\therefore n(A\cap B)=4$
$\Rightarrow n(A-B)=n\left(A\right)-n(A\cap B)=20-4=16$

Similarly, $n(B-A)=n\left(B\right)-n(A\cap B)=6-4=2$