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Math Help - empty set

  1. #1
    Junior Member
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    Dec 2008
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    empty set

    is the empty set reflexive? like it's vacuously symmetric and transitive?
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Paris
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    Hi
    Do you mean, as a relation, considering that \emptyset\times\emptyset=\emptyset?

    In that case, that would be true iff the set A used for the relation is empty:
    \forall x\in\emptyset,\ (x,x)\in\emptyset is true, while
    \forall x\in A,\ (x,x)\in\emptyset is false when A has at least one element.
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