I'm trying to solve
"If R is a relation on Z so that aRb if b=a+3 then how many equivalence relations, S on Z contain R?"
I had originally thought none, but then found that if S is a=b (mod 3) then this is an equivalence containing R.
So now I don't know where to go next. Is this the only relation? So how do I show that? Can someone point me in the right direction?