You only need to do D please. Thanks (b) Define R* = R \ {0} and Q* = Q\ {0} Let E be the binary relation on R*defined byTES←qQ* such that qr = s.Prove that E is an equivalence relation.(c) For each rЄ R*, let [r] be the E-equivalence class which contains r; andlet R*/E = {[r] | r = R*} be the set of E-equivalence classes. Prove thatthe multiplication operation on R*/E given by[x] · [y] = [xy]is well-defined.(d) Determine whether R*/E is a countable or uncountable set.

Part (d): Determine whether R*/E is countable or uncountable*Restating the Setup:R = R \ {0}**: This…

Answered: (b) Define R* = R \ {0} and Q* = Q\ {0}…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

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