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Math Help - [SOLVED] Transitive relation help please?

  1. #1
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    [SOLVED] Transitive relation help please?

    Give a transitive relation R on {1,2,3,4} such that R^2={} ( {}=empty set). (R^2 refers to the composition RoR)

    How do I go about finding this relation? I tried, but ended up with the full set of all relations on the set I don't know what to do.

    Any input would be greatly appreciated.

    Thanks in advance.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by chocaholic View Post
    Give a transitive relation R on {1,2,3,4} such that R^2={} ( {}=empty set). (R^2 refers to the composition RoR)

    How do I go about finding this relation? I tried, but ended up with the full set of all relations on the set I don't know what to do.

    Any input would be greatly appreciated.

    Thanks in advance.
    What about (a, b) \in R \Leftrightarrow a+2 < b? It is clearly transitive, and the only relation it gives you is (1, 4). Its composition will give you no relations.
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