is the empty set reflexive? like it's vacuously symmetric and transitive?

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- Feb 15th 2009, 09:18 PMvassagoempty set
is the empty set reflexive? like it's vacuously symmetric and transitive?

- Feb 15th 2009, 11:35 PMclic-clac
Hi

Do you mean, as a relation, considering that $\displaystyle \emptyset\times\emptyset=\emptyset$?

In that case, that would be true iff the set $\displaystyle A$ used for the relation is empty:

$\displaystyle \forall x\in\emptyset,\ (x,x)\in\emptyset$ is true, while

$\displaystyle \forall x\in A,\ (x,x)\in\emptyset$ is false when $\displaystyle A$ has at least one element.