(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

On the set of integers, define the relation R by: aRb if ab>=0.

Is R an equivalence relation?

2. Relevant equations

3. The attempt at a solution

R is an equivalence relation if it satisfies:

1) R is reflexive

Show that for all a∈Z, aRa.

Let a∈Z. Then if a is a negative integer, aa>=0. If a is a positive integer, aa>=0. And if a = 0, aa>=0.

Hence aRa

I feel like it is too simple.. lacking something??

2) R is symmetric

Show that for all a∈Z, aRb --> bRa

Let a∈Z, b∈Z such that aRb. By the definition of R, ab>=0.

This is not symmetric. Take a = -1, b = 2.

Then we have ab = -2 which is not >= 0.

3) R is transitive

if aRb and bRc implies aRc for all a,b,c ∈ Z

Let a, b, c ∈ Z s/t aRb, bRc --> aRc

Now I think this one is true.. but I'm not sure. But since aRb, and bRc, then you would always have ab or bc >=0 yea? so that means aRc must be true..

How would I prove it properly if it is correct?

Any help is appreciated! :) Thanks.

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# Homework Help: Proving an equivalence relation

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