# 3. Let X and Y be countably infinite sets. (a) Prove: If X and Y are...

###### Question:

3. Let X and Y be countably infinite sets. (a) Prove: If X and Y are disjoint then XuY is countably infinite. (b) Is the statement in (a) still true if we remove the hypothesis that X and Y are disjoint? If yes, justify your reasoning with a few sentences. If no, provide a counterexample. (P.S. "Counterexample” means that you have to explain why the example you provide demonstrates that the statement is false.)

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