A Antisymmetric relation is a relationship that happens when for all a and b in X:
In mathematical notation, an Antisymmetric relation between x and y follows <MATH> y = f(x)\\ x \neq f(y) \\ x = f(y) \text{ only because } x = y </MATH>
Or in other word, if the relation is a asymmetric
Every asymmetric relation is antisymmetric.
When there is a direction on the association, the relationship is antisymmetric.
A antisymmetric relation in the set of {1,2,3} would be the set of tuple
<1,3>
<2,1>
<3,2>
<1,1>
<2,2>
<3,3>