   Chapter 8.3, Problem 40ES ### 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 equivalenve class without using the results of Lemma 8.3.2, Lemma 8.3.3, or Theorem 8.3.4. For every a , b , and x in A, if a R b and x ∈ [ a ]

To determine

To prove:

For all a, b, and x in A, if a R b and x ∈ [ a ], then x ∈ [ 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,bA and xA such that a R b and x[a].

By the definition of [a]={xA|x R a}:

x R a

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

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