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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
More about Equivalence Relations
Equivalence relations have three strong prop erties, and they define strong ties between the elements of a
set. The elements that are in relation with each other can all be grouped in a special set, called an equiva-
lence class. Lets examine the precise definition of these sets .
Let A be a set and R an equivalence relation defined on A. Let x A.IfxRy, the ele ments x and y are
said to be equivalent. The equivalence class of x determined by R is the set
½x= fa A jaRxg:
EXAMPLE 4.3.11
Consider again the relation in Example 4.3.8, where A = {1, 2, 3, 4} and the relation is
aRb if and only if a b is an even number ...
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Publisher Resources

ISBN: 9780123822178