Answered: 1. (p.209, #16) Define a relation R on…

1. (p.209, #16) Define a relation R on Z by declaring that xRy if and only if x? = y? (mod 4). Prove that R is reflexive, symmetric and transitive.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 23E: 23. Let be the equivalence relation on defined by if and only if there exists an element in ...

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1. (p.209, #16) Define a relation R on Z by declaring that xRy if and only if x? = y? (mod 4).
Prove that R is reflexive, symmetric and transitive.

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