I saw that similar questions have been answered on this site, but I've been unable to translate those answers to my problem.
$$L=\{ww^R\mid w \in \{a,b\}^*\}$$
This is what I tried:
BWOC, assume that $L$ is regular. Then by M-N theorem, $L$ has a finite number of equivalence classes. Let $x$ and $y$ be strings, $x \neq y$, such that $[x]=[y]$.
This is where I get stuck. What would be the next step in tackling this? Is there a way to do this without contradicting it?
Consider the set of strings $\{a^nb : n\in\mathbb{N}\}$; that is, the set $\{ab, aab, aaab, \ldots\}$. Can you show that no two strings in this set can be in the same equivalence class?