Mark each statement True or False. Justify each answer.(a) A nonempty set S is countable i...

Mark each statement True or False. Justify each answer.

(a) A nonempty set S is countable iff there exists an injection

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(b) The set  of rational numbers is denumerable.

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

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(d) The set  of real numbers is denumerable.

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(e) |S| ≤ |T| means that there exists an injection

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