   Chapter 8.3, Problem 38ES ### 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 c in A, if b R c and c ∈ [ a ] then b ∈ [ a ] .

To determine

To prove:

For all a, b and c in A, if b R c and c ∈ [ a ] then b ∈ [ 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,bA and cA such that b R c and c[a]

By the definition of [a]:

[a]={xA|x R a}

Since c[a]:

c R a

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

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