Question: a) Prove that every convex set in Rn is connected. b) Show that the converse of part a) is false. c) Suppose that f: R

a) Prove that every convex set in Rn is connected.
b) Show that the converse of part a) is false.
c) Suppose that f: R → R. Prove that f is convex (as a function) if and only if E: = {(x, y): y > f(x)} is convex (as a set in R2).

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