Let S ⊆ ℝ. Mark each statement True or False. Justify each answer.
(a) int S ∩ bd S = ∅
(b) int S ⊆ S
(c) bd S ⊆ S
(d) S is open iff S = int S.
(e) S is closed iff S = bd S.
(f) If x ϵ S, then x ϵ int S or x ϵ bd S.
(g) Every neighborhood is an open set.
(h) The union of any collection of open sets is open.
(i) The union of any collection of closed sets is closed.
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