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Unformatted text preview: the purported identity isn't always true.) 5.2.4 The following is a proof that for all sets A and B, if A B, then A B B. Proof: Suppose A and B are any sets and A B. [ We must show that A B B. ] ] Let x A B. [ We must show that x B. ] By the definition of the union A B, either: (i) x A, or ii) x B. In the first case, x A, so by the definition of A B, x B. In the second case, x B. Thus, in both cases, x B. We have shown in general that if x A B, then x B. Therefore, by the definition of subset, A B B....
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This note was uploaded on 11/01/2010 for the course INFS 501 taught by Professor Ellis,w during the Spring '08 term at George Mason.
- Spring '08