Question

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

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (A)

$2$

Given: $n\left(X\right)=17,n\left(Y\right)=23$ and $n(X\cup Y)=38$

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

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

$\therefore n(X\cap Y)=2$.