Mark each statement True or False. Justify each answer. (a) Every nonempty subset of contains a minimum. (b) Every nonempty subset of contains a maximum. (c) If x and y are irrational, then x y is...

Mark each statement True or False. Justify each answer.

(a) Every nonempty subset of

contains a minimum.

(b) Every nonempty subset of

contains a maximum.

(c) If x and y are irrational, then x y is irrational.

(d) Between any two unequal rational numbers there is an irrational number.

(e) Between any two unequal irrational numbers there is a rational number.

(f ) The rational and irrational numbers alternate, one then the other