Let R be the relation on the set of integers defined as aRb + 5a + 8b = 0 (mod 13). (a) Show that R is an equivalence relation on Z. (b) Determine the equivalence class [7)R- (c) Is R an antisymmetric relation? If yes then explain why, if no then give a valid counter example.

Let R be the relation on the set of integers defined as aRb + 5a + 8b = 0 (mod 13). (a) Show that R is an equivalence relation on Z. (b) Determine the equivalence class [7)R- (c) Is R an antisymmetric relation? If yes then explain why, if no then give a valid counter example.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 8E: In Exercises 610, a relation R is defined on the set Z of all integers. In each case, prove that R...

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Let R be the relation on the set of integers defined as
aRb + 5a + 8b = 0 (mod 13).
(a) Show that R is an equivalence relation on Z.
(b) Determine the equivalence class [7)R-
(c) Is R an antisymmetric relation? If yes then explain
why, if no then give a valid counter example.

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