For homework I am supposed to prove a proposition that says: Assume we are given an equivalence relation on set A.
For a1 and a2 in A either [a1] = [a2] or [a1] intersect [a2] = the empty set.
where [a1] means the equivalence class of a1 in A and the or is inclusive.
i tried breaking it up into cases one case where [a1] = [a2] and the other where if [a1] did not = [a2] the [a1] intersect [a2] must = the empty set. But apparently that wasn't correct.
Can anyone help??? I'd really appreciate it.