~RLet ~ be the relation on Z given by a ~R b if and only if there exists c € Z withgcd (c, 17) = 1 such that a = c²b (mod 17).(a) Show that ~R is an equivalence relation.(b) Identify the equivalence classes of ~R.

A relation which is reflexive symmetric and transitive.

Answered: Let ~R be the relation on Z given by a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Let ~R be the relation on Z given by a ~R b if and only if there exists ce Z with ged(c, 17) = 1 such that a = c²b (mod 17). (a) Show that ~R is an equivalence relation. (b) Identify the equivalence classes of ~R.