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Homework 2 Solutions Math 171, Spring 2010 Henry Adams The exercises are from Foundations of Mathematical Analysis by Richard Johnsonbaugh and W.E. Pfaf-fenberger. 9.6. Prove that if Aand Bare countable sets, then A Bis countable. Solution. For a xed a 2A, let B a = f(a;b) 2A B jb 2Bg. Since B is countable, each B ais countable. Note that [a2AB ais the countable union of countable sets, and ...

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