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Math Help - Union of Transitive Relations

  1. #1
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    Union of Transitive Relations

    What would a counterexample look like to prove the union of two transitive relations on the same set need not be transitive?
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    On the set \left\{ {a,e,i,o,u} \right\} both R = \left\{ {\left( {a,e} \right)} \right\}\,\& \,S\left\{ {\left( {e,i} \right)} \right\} are transitive.
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