I have a similar question that is posted here:
But I don't understand the answers that people gave there.
I have seen some where that when you have the set S = {x,y,z} that the equivalence relation could be the following pairs: {(x,x), (y,y), (z,z)}
I don't see how to show that this is symmetric and transitive.
In the link one person stated that it is "vacuously" because we essentially can't test for symmetric and transitive. Well, if we need all of the 3 conditions to be met, and we can't apply 2 of them, then I am thinking that we hence can't call it an equivalence relation!
SO not sure how the logic of this goes! Hope someone can shed some light on this.