Languages having only one Myhill–Nerode equivalence class Consider the alphabet $\{a,b\}$, for which languages does the Myhill&ndash;Nerode equivalence relation have exactly one class? 

From what I understand about equivalence classes, each state is considered a class. So would $\{ a^n : n&gt;0\}$ be the one class?
Assuming that you mean the Myhill-Nerode relation, the Myhill-Nerode theorem states that the number of equivalence classes exactly equals the number of states in the minimal DFA accepting the language (if it's regular; otherwise there are infinitely many equivalence classes). So we have reduced the question to the following one:


  Which regular languages can be accepted using a DFA having only one state? 


I'm sure you can answer this one yourself.