(a) Give explicit examples, with justification, of a language over some finite alphabet $\Sigma$ which is:

(i) context-free, but not regular;

(ii) recursive, but not context-free.

(b) Give explicit examples, with justification, of a subset of $\mathbb{N}$ which is:

(i) recursively enumerable, but not recursive;

(ii) neither recursively enumerable, nor having recursively enumerable complement in $\mathbb{N}$.