Can you write an example of such a maximum relation for n = 3 or n = 4?
Do you know how to make a table of ordered pairs?
That is on a set of three elements. There are pairs.
So there are possible relations on a set of three.
When is a relation not antisymmetric?
There is a start.
If you are unable to carry on, then you need to go to instructor for face-to-face help.