Equivalence Relations on the Set of Integers - Homework Solution

[eiselea]

Homework Statement

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?

Homework Equations

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.

 

[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??