How can I find the Myhill-Nerode classes for the language A?
Two strings $x$ and $y$ are in the same Myhill&ndash;Nerode class if they can't be distinguished by adding the same string onto the end of them. That is, they're in the same class if, for all strings&nbsp;$z$, either $xz$ and&nbsp;$yz$ are both in the language or neither of them is.

So, for example, the strings $00$ and $01$ are in different classes because we can distinguish then by adding&nbsp;$1$: $001$ is in the language and $011$ is not.  In fact, they're already distinguished by the empty string&nbsp;$\epsilon$, since $01$ is in the language but $00$ is not.

In your case, you can shortcut this because the notion of indistinguishability corresponds exactly to minimal automata: the classes are exactly the sets of strings that take you to each state of the automaton.