Mark each statement True or False. Justify each answer.
(a) If a nonempty subset of ℝ has an upper bound, then it has a least upper bound.
(b) If a nonempty subset of ℝ has an infimum, then it is bounded.
(c) Every nonempty bounded subset of ℝ has a maximum and a minimum.
(d) If m is an upper bound of S and m'<m, then m' is not an upper bound of S.
(e) If m = inf S and m'<m, then m' is a lower bound of S.
(f) For each real number x and each ε > 0, there exists n ϵ ℕ such that nε > x.
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