# Thread: how to determine whether transitive

1. ## how to determine whether transitive

for this digraph since two of the vertices on the top right and bottom left are not connected to anything will this digraph be not transitive???

2. ## Re: how to determine whether transitive

let $X$ and $Y$ be elements of your set. you have to show that

$(g~ R~ X) \wedge (X~ R~ Y) \Rightarrow (g ~R ~Y)$

then only element $X \ni (g~ R~ X)=True$ is $X=g$

so you are reduced to determining if

$(g~ R~ g) \wedge (g~ R~ g) \Rightarrow (g~ R ~g)$ which is trivially true if reflexion hold which in this case does.

The case for $c$ is identical.