Prove that the following languages are not regular.
(a) $L =$ {$a^nb^la^k : k ≥ n + l$}.
(b) $L =$ {$a^nb^la^k : k ≠ n + l$}.
(c) $L =$ {$a^nb^la^k: n = l$ or $l ≠ k$}.
(d) $L =$ {$a^nb^l : n ≤ l$}.
(e) $L =$ {$w: n_a (w) ≠ n_b (w)$ }.
(f) $L =$ {$ww : w ∈${$a, b$}$^*$}.
(g) $L =$ {$wwww^R : w ∈$ {$a, b$}$^*$}.
