Let $D$ be a dense in $X$. Prove that for every open set $U\subseteq X$, $\newcommand{\cl}{\operatorname{cl}}\cl (D \cap U) = \cl(U)$
For my solution, what I did is by showing that the $\cl(D \cap U)$ is contained in $\cl(U)$ and vice versa.
I've done the $\subseteq$. I have trouble in the $\supseteq$ part.
or is their an easier solution where I don't need the inclusions?