Originally Posted by

**iwish123** The relation T is defined on the set of integers by:

aTb if and only if ab>0 or a=b=0

For the equivalence realtion I have come up with the following

1. Reflexive: aTa as a=a=0 or we could have stated that aa>0

2. Symmetric: Take integers a,b. aTb means ab>0 or a=b=0 => b=a=0 or ba>0. Hence we also have bTa

3. Transitive: Take integers a,b,c. If we have aTb and bTc, ab>0 or a=b=0 and bc>0 or b=c=0. So we have a=b=c=0, hence, bTc

Then, the next question I was asked was what are the equivalence relations?