Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Is this sufficient for a relation to be transitive
  1. Fading Transition (Replies: 36)

  2. Transitive Relations (Replies: 1)

  3. Making the Transition (Replies: 2)

Loading...