If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩Y).

It is given that:

n(X) = 17, n(Y) = 23, n(X ∪ Y) = 38

n(X ∩ Y) = ?

We know that:

$n(\mathrm{X} \cup \mathrm{Y})=n(\mathrm{X})+n(\mathrm{Y})-n(\mathrm{X} \cap \mathrm{Y})$

$\therefore 38=17+23-n(\mathrm{X} \cap \mathrm{Y})$

$\Rightarrow n(\mathrm{X} \cap \mathrm{Y})=40-38=2$

$\therefore n(\mathrm{X} \cap \mathrm{Y})=2$