My Professor Gave an example in class when we were learning about equivalence relations:
He said this example did not fulfill the Reflexive Property of Relations, and I can't figure out why:
Reflexive Property : ∀s ∈ S (s,s) ∈ T
Let S be the set of students in this room. Then, for s,t ∈ S we say that s ≡ t if s and t do not have the same birthday.
Because even if my birthday is or is not the same as someone else's, it is still my birthday right?
(the example may be awkward because the professor reversed an equivalence statement to give a relation that was non-equivalent)
Any explanation is welcome.