Question

If $X$ and $Y$ are two sets such that $n\left(X\right)=20,n\left(Y\right)=25\text{and}n\left(XUY\right)=40$, $thenn(X-Y)=$

• A. $20$
• B. $15$
• C. $40$
• D. $5$

Answer 1

The correct option is B $15$

$\mathrm{We}\mathrm{know}\mathrm{that}n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)\Rightarrow 40=20+25-n(X\cap Y)\Rightarrow n(X\cap Y)=5X-Y=X-(X\cap Y)\therefore n(X-Y)=n\left(X\right)-n(X\cap Y)\Rightarrow n(X-Y)=20-5=15$