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I know that for transitive relation if $(A,B)$ and $(B,C)$ exist then $(A,C)$ must also exist but the problem is that

  • If I see $(a,b)$ and $(b,a)$ exist then $(a,a)$ should exist and yes it does, so transitive.
  • If I see $(b,a)$ and $(a,b)$ then $(b,b)$ should exist which does not, so not transitive.
Angelo
  • 12,328
PF 49 Prajjwal Singh
  • 21

1 Answers1

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For a relation to be transitive, it must be the case that whenever you see $(x, y)$ and $(y, z)$, you should also see $(x, z)$.

So even the existence of one pair not satisfying that is sufficient to say that it is not transitive. (Even if there are tons of other pairs which do satisfy it.)

So, in your case, the relation is not transitive.

Aryaman Maithani
  • 15,771