Let S ⊆ ℝ. Mark each statement True or False. Justify each answer.
(a) bd S = bd (ℝ\S)
(b) bd S ⊆ ℝ\S
(c) S ⊆ S' ⊆ cl S
(d) S is closed iff cl S ⊆ S.
(e) S is closed iff S' ⊆ S.
(f) If x ϵ S and x is not an isolated point of S, then x ϵ S'.
(g) The set ℝ of real numbers is neither open nor closed.
(h) The intersection of any collection of open sets is open.
(i) The intersection of any collection of closed sets is closed.
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