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Math Help - Relation proof

  1. #1
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    Relation proof

    Use the logical definition to explain why the null relation is transitive.




    The only thing that makes sense to me is that it doesnt violate the rules of transitivity, so im assuming that it is transitive, but this is clearly not a proof, so need some help.
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  2. #2
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    Quote Originally Posted by tokio View Post
    Use the logical definition to explain why the null relation is transitive.
    This proof turns on a simple fact of logic: "A false statement implies any statement."
    If P is a false statement the the statement 'If P then X' is a true statement no matter what statement X is.

    If \mathbb{E} is the empty relation then (a,b) \in\mathbb{E}~\&~(b,c) \in\mathbb{E} is always false.
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