Question

Let A and B be two sets such that $n\left(A\right)=20,n(A\cup B)=42\text{and}$
$n(A\cap B)=5,$ then $n(B-A)=$

• A. $18$
• B. $20$
• C. $22$
• D. $27$

Answer 1

The correct option is C $22$

Given two sets $A\&B$ such that:
$n\left(A\right)=20,n(A\cup B)=42\text{and}$
$n(A\cap B)=5$
Using the formula:

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)\Rightarrow 42=20+n\left(B\right)-5\Rightarrow n\left(B\right)=27\because n(B-A)=n\left(B\right)-n(A\cap B)\Rightarrow n(B-A)=27-5=22$