Let fi : R" –→ R and f2 : R" → R be two functions. (5.1) Consider the following proposition: If epi(fi) N epi(f2) is a convex set, then at least one of the functions fi and f2 is a convex function. Either prove this proposition or give a counterexample (i.e., find two functions fi : R" and f2 : R" → R that satisfy the hypothesis but do not satisfy the conclusion).

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