Mark each statement True or False. Justify each answer. (a) A nonempty set S is countable iff there exists an injection f :  → S. (b) The set Q of rational numbers is denumerable. (c) Let S be a...

Mark each statement True or False. Justify each answer.

(a) A nonempty set S is countable iff there exists an injection f :
 → S.

(b) The set Q of rational numbers is denumerable.

(c) Let S be a nonempty set. There exists an injection f : S →
 iff there exists a surjection g :
 → S.

(d) The set R of real numbers is denumerable.

(e) | S | ≤ | T | means that there exists an injection f : S → T.

(f ) The continuum hypothesis says that ℵ0 is the smallest transfinite cardinal number.