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 if Y is closed. (ii) Let X and Y be sets from Rn. If X Y is closed and convex then either X 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 then X 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.