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Is this sufficient for a relation to be transitive

  1. Jan 21, 2008 #1
    in the book i'm reading it gives a set S={0,1,2,3}, and it says that the relation R where (m,n) [tex]\in[/tex] R if m + n = 3, m,n [tex]\in[/tex] S.

    it says that this relation isn't transitive, but couldn't you give a vacuous argument for transitivity.

    more specifically there are no x,y,z s.t. (x,y) and (y,z) are elements of the S, therefore the statement
    if (x,y) and (y,z) are in S then (x,z) is in S should be true, right?
  2. jcsd
  3. Jan 21, 2008 #2
    (0,3) and (3,0) are both in R, but (0,0) is not.
  4. Jan 21, 2008 #3
    thanks, i don't know how i missed that. i must have had myself fooled that the 3rd number had to be unique from the first, when clearly it doesn't.
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