Answer the following questions on equivalence relation and partial order. Note: If you claim that a relation has a specific property which makes it a partial order or an equivalencerelation, please explain why you think that the relation has that claimed property. For example, if you claimthat a relation is symmetric, you should explain why you think that the relation is symmetric. Follow thesame line of argument for all properties. Give examples and/or counterexamples when needed.a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides a-b). Is Ran equivalence relation? Why or why not? Justify your answer.

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Answered: a) Relation R is defined on Z as…

a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides a-b). Is R an equivalence relation? Why or why not? Justify your answer.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...

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Question

Answer the following questions on equivalence relation and partial order.

Note: If you claim that a relation has a specific property which makes it a partial order or an equivalence
relation, please explain why you think that the relation has that claimed property. For example, if you claim
that a relation is symmetric, you should explain why you think that the relation is symmetric. Follow the
same line of argument for all properties. Give examples and/or counterexamples when needed.
a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides a-b). Is R
an equivalence relation? Why or why not? Justify your answer.

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