Hello, I have the following problem, I think I've proved the equivalence relaltion correctly, but cannot figure out how to work the equivalence classes. Hopefully some one will know!
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?