If $A$ is a set $\{2,4,6,8\}$, and we are asked to give a relation on $A$ that is:
symmetric, antisymmetric, but not reflexive, is this possible?
If we were to say $\{(2,2),(4,4)\}$, it would indeed be symmetric and antisymmetric, but it would also be reflexive.
If we were to say $\{(2,2),(4,4),(6,8)\}$, this would not be symmetric.
I'm thinking that this isn't possible, but would like to know others' thoughts.
Best Answer
Ah, but $\{ (2,2), (4,4) \}$ isn't reflexive on the set $\{2,4,6,8\}$ because, for example, $(6,6)$ is not in the relation.