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Math Help - how to determine whether transitive

  1. #1
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    how to determine whether transitive

    how to determine whether transitive-hhhh.png
    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???
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  2. #2
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    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.
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