Question

If X and Y are two sets such that $n\left(X\right)=17,n\left(Y\right)=23$ and $n(X\cup Y)=38$, find $n(X\cap Y)$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

$n(X\cup Y)=n\left(X\right)+n\left(Y\right)-n(X\cap Y)$

$38=17+23-n(X\cap Y)$

$n(X\cap Y)=40-38=2$