Let $\Sigma = \{a, b\}$. For a word $w \: \: \in \Sigma^*$ let $n_a(x)$ denote the number of $a$'s in $w$ and let $n_b(x)$ denote the number of $b$'s in $w$. Consider the following language:
$L:=\{ xy \mid x, \: y \in \Sigma^*, \: \: n_a(x) = n_b(y)\}$
What can we say about $L$?
- $L$ is regular, but not context-free
- $L$ is context-free, but not regular
- $L$ is $\Sigma^*$
- None of these