Is a set Anti-Symmetric if it's all reflexive? Lets say I have a set of integers of $-7\ to \ 7$
And $ R = {(a,b)|a^3=b^3} $
I don't understand anti-symmetry fully and I'm wondering if a set is only reflexive then it must be anti-symmetric?
Also is it:
Reflexive?
Symmetric?
Anti-symmetric?
Transitive?

Use the squares, not cubes in your example. This equivalence relation is reflexive, but is't antisymmetric: $(-6)R(6) ~\&~ (6)R(-6)~ \& ~(-6 \ne 6  )$
