Let $\displaystyle A$ and $\displaystyle C$ be subsets of $\displaystyle R^n$ with boundaries $\displaystyle B(A)$, $\displaystyle B(C)$ respectively.

Prove or disprove:

- $\displaystyle B(A\cup C)=B(A)\cup B(C)$
- $\displaystyle B(A\cap C)=B(A)\cap B(C)$

I haven't gotten to look much at boundaries yet, so I could use a hand.