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Unformatted text preview: C ) implies x ( A B ) ( A C ) . To prove part 2, we must prove that x ( A B ) ( A C ) implies x A ( B C ) . In this case the proof is simple, since it just follows the above proof in reverse. The details are left as an exercise. The above proof is an example of the generality often required to prove a property about sets: it uses arbitrary sets and arbitrary elements of such a set. In contrast, to show that a property is false, it is enough to Fnd one counterexample. Such counterexamples should be as simple as possible, to illustrate that a statement is not true with minimum effort to the reader. P ROPOSITION 2.7 The following statements are not true: 1. A ( B C ) = ( A B ) C ; 2. A ( B C ) = ( A B ) ( A C ) . 9...
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 Spring '09
 Koskesh
 Math, Logic, Sets

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