1. The problem statement, all variables and given/known data I'm trying to prove that the boundary of the union of two sets is a subset of the union of the boundaries of the two sets. i.e. Show that B(X u Y) c= B(X) u B(Y). 2. Relevant equations 3. The attempt at a solution Since I didn't know what to do here, I used the identity A c= B <==> cl(B) c= cl(A), and then a lot of set algebra to prove it. Given how simple the statement looks, I'm wondering if there is an easier way. Thanks.