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October 19th, 2012, 06:22 AM   #1
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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?
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October 19th, 2012, 07:44 AM   #2
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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?
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October 20th, 2012, 01:38 PM   #3
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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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