1 answer

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 stat

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.)

Answers

(9) lexx and i are disjoint Bence x and y ane Gountable then Welan write Xz2 a, az, az... } 1 Y=231, 32, 63 ... } Define folNt ęs a subset of Y. So as is either finite of contable. If Az istinite Then AUA, is the Union of an Corntalle set and a finit

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