   Chapter 8.3, Problem 39ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let R be an equivalence relation on a set A. Prove each of the statements in 36-41 directly from the definitions of equivalence reation and equivalence class without using the results of Lemma 8.3.2, Lemma 8.3.3, or theorem 8.3.4. For every a and b in A, if [a]=[b] then aRb.

To determine

To prove:

For all a and b in A, if [ a ] = [ b ] then a R b.

Explanation

Given information:

Let R be an equivalence relation on a set A.

Proof:

R is an equivalence relation on a set A.

Let aA and let bA such that[a]=[b].

In one of the previous exercises, we showed that a[a] (which followed from the reflexive property of R and the definition of [a]={xA|x R a}).

a[a]

Since [a]=[b]:

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