. For each of the following, state whether it is true or false. If true, prove. If false, provide a counterexample.

(i) Let X and Y be sets from Rn. If X Y then X is closed if and only ifY is closed.

(ii) Let X and Y be sets from Rn. If X Y is closed and convex then eitherX or Y is closed and convex (one or the other).

(iii) Let X be an open set and Y X. If Y , then Y is a convex set.

(iv) Suppose X is an open set and Y is a convex set. If X Y X thenX Y is open.(v) If A and B are closed sets, and A B = then A B is a closed set.(vi) If a set A is closed, then A cannot be open.