Suppose you have two infinite sets A and B with the following properties They are disjoint --i.e., A intersection B = phi They are both (infinitely) countable Your task: show that A Union B must also be countable. | How to set up your proof State what you know about sets A and B -- something that starts like (1) "since A is countable, we know that there exists....." and (2) "since B is countable, we know that there exists...." Now state what you must show about A Union B -- something that starts like "in order to show that AUnion B is countable, we will show that there exists....." (In the above, it is of course up to you to correctly complete the setup statements). Up to now, everything is just setup, now it is up to you to show what you set out to show in (3)