Let C={x:x^3∈Z}C={x:x^3∈Z}. (a) Show that C∩Q≠∅C∩Q≠∅. (Ie. show C contains a rational.) (b) Prove that C∩R∖Q≠∅C∩R∖Q≠∅. (Ie. show C contains an irrational.) (c) Prove C is countable. (d) Is R∖C countable or uncountable? Justify your answer.

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