Determine whether or not the following languages on $Σ =$ {$a$} are regular.
(a) $L =$ {$a^n: n ≥ 2,$ is a prime number}.
(b) $L =$ {$a^n: n$ is not a prime number}.
(c) $L =$ {$a^n: n = k^3$ for some $k ≥ 0$}.
(d) $L =$ {$a^n: n = 2^k$ for some $k ≥ 0$}.
(e) $L =$ {$a^n: n$ is the product of two prime numbers}.
(f) $L =$ {$a^n: n$ is either prime or the product of two or more prime numbers}.
(g) $L^*$, where $L$ is the language in part $(a)$.
