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October 19th, 2012, 06:22 AM  #1 
Newbie Joined: Oct 2012 Posts: 1 Thanks: 0  Abstract Algebra: Groups and Subgroups Problem
Let R be the set of real numbers. Determine whether the relation H on R defined as xHy <=> y=kx for an integer k, is (a) reflexive (b) symmetric (c) transitive Is H an equivalence relation? 
October 19th, 2012, 07:44 AM  #2 
Senior Member Joined: Nov 2011 Posts: 100 Thanks: 0  Re: Abstract Algebra: Groups and Subgroups Problem
What have you tried so far? What can you tell me about the relation between some relation satisfying a,b,&c and being an equivalence relation?

October 20th, 2012, 01:38 PM  #3 
Senior Member Joined: Jul 2011 Posts: 227 Thanks: 0  Re: Abstract Algebra: Groups and Subgroups Problem
(a) It's clear that therefore the relation is reflexive. (b) We have but (only if or but the statement has to be true for every ) thus not symmetric. (c) We have and also thus and because we have so the relation is transitive. It's not an equivalence relation because only (a) and (c) are satisfied. 

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