If \(\sim\) is an equivalence relation on a nonempty set \(A\), then for all \(a \in A\), the set \([a]\) is nonempty.

If \(\sim\) is an equivalence relation on a nonempty set \(A\), then for all \(a, b \in A\), \(a \sim b\) if and only if \([a] = [b]\).

If \(\sim\) is an equivalence relation on a nonempty set \(A\), then for all \(a, b \in A\), either \([a] = [b]\) or \([a] \cap [b] = \emptyset\).