Mark each statement True or False. Justify each answer. (a) If a nonempty subset of has an upper bound, then it has a least upper bound. (b) If a nonempty subset of has an infimum, then it is...

Mark each statement True or False. Justify each answer.

(a) If a nonempty subset of

has an upper bound, then it has a least upper bound.

(b) If a nonempty subset of

has an infimum, then it is bounded.

(c) Every nonempty bounded subset of

has a maximum and a minimum.

(d) If m is an upper bound of S and m′ <>

(e) If m = inf S and m′ <>

(f ) For each real number x and each ε > 0, there exists n ∈

such that nε > x.