   Chapter 8.3, Problem 36ES ### 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 Lemma 8.3.2, Lemma 8.3.3, or Theorem 8,3,4. For every a in A , a ∈ [ a ] .

To determine

To prove:

For all a in A, a ∈ [ a].

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.

Since R is an equivalence relation, R is reflexive, symmetric and transitive.

By the definition of reflexive:

(a,a)R or equivalently a R a

By the definition of [a] :

[a]={

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