Question

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

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

Answer 1

The correct option is C $22$

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