Antisymmetric: (2, 1) is in the set. If this relation is antisymmetric, (1, 2) must not be in the set. Yes this is true. So, this property is true.

I was giving an example! (2,1) is not the only pair you need to check.
Reflexive Property:
If x in an element in R, then x < x for all x in R. Therefore, x precedes x.

You mean x<= x (or [itex]x\le x[/tex]), of course.