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  1. A transitive and connected relation is a negative transitive?

  2. A negative transitive and asymmetric relation is transitive?

Is this correct for 2?
Assume that R be transitive and connected relation but is not a transitive
(if $(a,b) \in R$ and $(b,c)\in R$ we have not $(a,c)\in R$).
So for every a,b:

$(a,b) \notin R$ from connected $(b,a)\in R$,

$(b,c) \notin R$ from connected $(c,b)\in R$.

From above and transitive we have $(c,a)\in R$ . what should I do next?

How can I show 1 is true?

linkho
  • 397
  • In the problem statement for 2, you say negative transitive and asymmetric, but in the proof you use negative transitive and connected. Which is it? As for 1, consider the trivial relation, i.e. the relation where every single available pair is an element. – Arthur Oct 20 '17 at 06:39
  • @Arthur hello, You're right, I changed it. Thank you – linkho Oct 20 '17 at 09:54

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