Let $\displaystyle A$ and $\displaystyle B$ be subsets of $\displaystyle \Re^n$ with $\displaystyle A^0$, $\displaystyle B^0$ denoting the sets of interior points for $\displaystyle A$ and $\displaystyle B$ respectively. Prove that $\displaystyle A^0\cup B^0$ is a subset of the interior of $\displaystyle A\cup B$. Give an example where the inclusion is strict.