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Math Help - Relations (double check?)

  1. #1
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    Relations (double check?)

    A binary relation P is defined on Z as follows: For all m, n \in Z 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 m, n \in Z to n, m \in Z 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?
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    Quote Originally Posted by Open that Hampster! View Post
    A binary relation P is defined on Z as follows: For all m, n \in Z 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 m, n \in Z to n, m \in Z 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?
    Is it true that (2,10)\in\mathcal{P}~\&~(10,25)\in\mathcal{P}~?
    Is it the case that (2,25)\in\mathcal{P}~?
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