Trying to understand transitive relations

[r0bHadz]

Homework Statement

Say you have relation R= {(2,4) (4,2)}

Relevant Equations

If (a,b) is an element of R, and (b,c) is an element of R, R={(a,b) (b,c) (a,c)} is transitive

Obviously R is not transitive because it doesn't contain (2,2). But does it need to contain both (2,2) and (4,4) to be considered transitive?

 

[Dick]

Yes. A better definition of transitivity would say if $(a,b)$ and $(b,c)$ are elements of $R$, then $(a,c)$ is an element of $R$. It has to hold for ALL $a$ and $c$, the case $a=c$ included.

 

[r0bHadz]

thanks for the reply. I can't figure this new design out at all, not sure where the "answered" button is