Question

If X and Y are two sets such that n(X) = 20, n(Y) = 25 and n(X U Y) = 40, then n(X - Y) =

• A. 20
• B. 15
• C. 40
• D. 5

Answer 1

The correct option is B 15

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