# Thread: empty set

1. ## empty set

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

2. 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.