Equivalence relations

[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\geq0. 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

[quasar987]

You must check 3 things:

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

[eiselea]

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

[quasar987]

But you haven't explained anything.

1) Why does aRa for every integer a??