2. If F is a closed set and G is an open set in a metric space M, show that F \\ G is closed and that G \\ F is open. 3. Some authors say that two metrics d and p on a set M are equivalent if they generate the same open sets. Prove this. (Recall that we have defined equivalence to mean that d and p generate the same convergent sequences. See Exercise 3.42.)D 5. Let f : R - R be continuous. Show that (x : f(x) > 0) is an open subset of R and that (x : f(x) = 0) is a closed subset of R