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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
1. We proved that the equality A (B C)=(A B) C does not hold true, and the sets in Example 4.1.6
provide a counterexample for it.
2. On the other hand, at least in this example A (B C)=(A B) (A C). Is this equality true by
chance for the sets used in the example, or does it hold true for any choice of the three sets?
Lets try to prove this second result.
EXAMPLE 4.1.7
If A, B, and C are any three sets, then
A ðB CÞ= ðA BÞ ðA CÞ:
(This is known as the distributive property of the intersection with respect to the union.)
Proof: Part 1. A (B C) (A B) (A C)
Let x A (B C). We want to pr ove that x (A B)
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Publisher Resources

ISBN: 9780123822178