Answered: Let R={(a,b)∈R×R: there is an integer k…

Let R={(a,b)∈R×R: there is an integer k s.t. a−b= 2kπ}. (a) Prove that R is an equivalence relation on R. (b) List 3 members of [π/4]. (c) List 3 members of [1]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3TFE: True or False Label each of the following statements as either true or false. If is an equivalence...

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Question

Let R={(a,b)∈R×R: there is an integer k s.t. a−b= 2kπ}.

(a) Prove that R is an equivalence relation on R.

(b) List 3 members of [π/4].

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