5.2.13 Solution

5.2.13 Solution - B C, x B C. In the second case, x C....

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INFS 501 - Problem 5.2.13 The following is a proof that for all sets A, B, and C, if A B, then A C B C. Proof : Suppose A, B, and C are any sets and A B. Let x A C. By the definition of the union A C, either: (i) x A, or ii) x C. In the first case, x A, and by the definition of A B, x B. Now, by the definition of
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Unformatted text preview: B C, x B C. In the second case, x C. Again by the definition of B C, x B C. Thus, in both cases, x B C. We have shown in general that if x A C, then x B C. Therefore, by the definition of subset, A C B C....
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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.

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