Let $S = \{a, b\}$ and let $X= \{w \mid \text{$w$ is a word over the alphabet $S$}\}$. For each language given below, list (if you can) two words which are in the language, and two words which are not in. (In either case, if there are no two such words, then explain why not.)
(a) $\{w ∈ X \mid \text{there are some $u, v ∈ X$ such that $uvw = wvu$}\}$
if $u = abb$, $v = baa$ and $w = ba$, $abbbaaba$ is not equal to $babaaabb$.
So how can every word over $S$ be in the language?