Mark each statement True or False. Justify each answer. (a) A set S is compact iff every open cover of S contains a finite subcover. (b) Every finite set is compact. (c) No infinite set is compact....

Mark each statement True or False. Justify each answer.

(a) A set S is compact iff every open cover of S contains a finite subcover.

(b) Every finite set is compact.

(c) No infinite set is compact.

(d) If a set is compact, then it has a maximum and a minimum.

(e) If a set has a maximum and a minimum, then it is compact.