A binary relation P is defined on Z as follows: For all m P n <=> exists a prime number p such that p|m and p|n
1) Is the relation reflexive?
2) Is the relation transitive?
3) Is the relation symmetric?
For 1 I'm assuming the answer's right, because if m = n then p|m must mean p|n. For 3 I'm assuming it is because going from to results in the same relationship.
What I'm not sure about is 2. I think it is transitive, because if x P y, and y P z, since P means p divides both parameters, then x P z must be valid as well.
I'm not entirely sure, but that's what I have so far. So it would be reflexive, transitive and symmetric?