# empty set

• February 15th 2009, 09:18 PM
vassago
empty set
is the empty set reflexive? like it's vacuously symmetric and transitive?
• February 15th 2009, 11:35 PM
clic-clac
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.