Question

If two sets $A$ and $B$ are such that $n\left(A\right)=20$, $n(A\cap B)=4$, and $n(A\cup B)=42$, then

• A. $n\left(B\right)=22$
• B. $n(B-A)=22$
• C. $n\left(B\right)=26$
• D. $n(A-B)=16$

Answer 1

Answer: (B), (C), (D)

$n(A-B)=16$

$n\left(A\right)=20,n(A\cap B)=4,n(A\cup B)=42$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$\Rightarrow 42=20+n\left(B\right)-4$
$\Rightarrow n\left(B\right)=26$

$n(B-A)=n\left(B\right)-n(A\cap B)=22$
$n(A-B)=n\left(A\right)-n(A\cap B)=16$