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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Is this sufficient for a relation to be transitive

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