Let S ⊆ . 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 ∈ S and x...

Let S ⊆
. 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 ∈ S and x is not an isolated point of S, then x ∈ 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.