Basic Set Theory: Determining Relations: Reflexive, Symmetric, Transitive

Bob4040
I am taking a philosophy course that covers basic set theory as part of the introduction. I’m not sure in which section of the forum set theory should be, but I think this is the right place.

Homework Statement

For each of the following relations, indicate whether it is Reflexive, Nonreflexive, Irrelfexive, Symmetric, Nonsymmetric, Asymmetric, Antisymmetric, Transitive, Nontransitive, and Intransitive.

9) {(b,d), (a,c), (d,c), (e,e), (b,c)} on the set {a,b,c,d,e}.

The Attempt at a Solution

I believe they are Nonreflexive, nonsymmetric, and transitive.

I do not know if they are Asymmetric or Antisymmetric because I do not know how to deal with (e,e).

Asymmetric: $xRy \Rightarrow \neg (yRx)$
Antisymmetric: $xRy \wedge yRx \Rightarrow x=y$