If X and Y are two sets such that $\mathrm{n}(\mathrm{X})=17$, $n(Y)=23$ and $n(X \cup Y)=38$, then

Question

If X and Y are two sets such that $\mathrm{n}(\mathrm{X})=17$, $n(Y)=23$ and $n(X \cup Y)=38$, then $n(X \cap Y)$ is equal to

Professor PC Thomas Classes · Answer

$n(A \cup B) = n(A) + n(B) - n(A \cap B) \implies 38 = 17 + 23 - n(A \cap B) \implies n(A \cap B) = 2$.