1. The problem statement, all variables and given/known data For each of the relations defined on ℚ, either prove that it is an equivalence relation or show which properties it fails. x ~ y whenever xy ∈ Z 2. Relevant equations 3. The attempt at a solution Here's my problem: I am starting off the proof with the first condition of reflexivity. Now, do I let x ∈ ℚ ? I would think so, if that is the case, then x can be 2/3. So xx is thus 4/9 which does not exist in the integers. Thus, the proof would fail. But I think I am missing something here. Did I do this right or am I making a fatal error by suggesting that x can be any ℚ?