# Equivalence relations

1. Feb 20, 2008

### eiselea

1. The problem statement, all variables and given/known data

Let S be the set of integers. If a,b$$\in$$ S, define aRb if ab$$\geq$$0. Is R an equivalence relation on S?

2. Relevant equations

3. The attempt at a solution

Def: aRb=bRa $$\rightarrow$$ ab=ba
assume that aRb and bRc $$\Rightarrow$$ aRc
a=b and b=c
since a=b, the substitute a in for b to get a=c

I don't know where to go from here.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 20, 2008

### quasar987

You must check 3 things:

1) That aRa (reflexivity)
2) That aRb implies bRa (symetry)
3) That aRb and bRc implies aRc (transitivity)

3. Feb 20, 2008

### eiselea

So what I have done so far answers the first part of the question?

4. Feb 20, 2008

### quasar987

But you haven't explained anything.

1) Why does aRa for every integer a??

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