   Chapter 8.3, Problem 37ES ### 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 relation and equivalence class without using the results of the Lemma 8.3.2, Lemma 8.3.3, or Theorem 8.3.4. For every a and b in A, if b ∈ [ a ] then aRb.

To determine

To prove:

For all a and b in A, if b ∈ [ a ] 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 b[a]

By the definition of [a]:

[a]={xA|x R a}

Since b

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