Recall that if A and B are two sets, we write A B if there exists...

  

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Recall that if A and B are two sets, we write A B if there exists a bijection f: A B. (a) Prove that A~ A. (b) Prove that if A B, then B~ A. (c) Prove that if A B and B~ C, then A~ C. These properties show that the relation A B is an equivalence relation. Recall that if A and B are two sets, we write A B if there exists a bijection f: A B. (a) Prove that A~ A. (b) Prove that if A B, then B~ A. (c) Prove that if A B and B~ C, then A~ C. These properties show that the relation A B is an equivalence relation.

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a Given any set A define the identity function IdA ... View the full answer