Do non-reflexive relations exist? I may be talking complete and utter trash here, but does there exist any relation that isn't by definition reflexive? I know anything must always be equal to itself but is there any way this can be shown as not true for a specific example?

The relation "$x$ and $y$ are not equal" on any set.

The relation "$x>y$" on a set of real numbers.

The relation "$x$ is the boss of $y$" on the set of people.