Q:

set-theory (anti-symmetric)

in relation, anti-symmetric -> if xRy and yRx, then x=y. 
Today, my lecturer said that relation $<$, which represents $(\le \bigwedge\ne)$, satisfies anti-symmetric. He did not prove it and He left it for us to exercise. I have no idea why anti-symmetric is satisfied when the relation is $<$.
Can anyone please explain? thanks

A:

I will assume that by $<$ you mean the "less than" relation on some totally ordered set such as the real numbers.
Is there ever a situation where you have $x<y$ AND $y<x$ at the same time?
No.
The statement then is an example of a Vacuous Truth since the premise is always false, there is no possible way that there is a contradiction.
A statement is only false if the premise is true while the conclusion is false.

