(a) State the pumping lemma for context-free languages (CFLs).

(b) Which of the following are CFLs? Justify your answers.

(i) $\left\{w w \mid w \in\{a, b, c\}^{*}\right\}$

(ii) $\left\{a^{m} b^{n} c^{k} d^{l} \mid 3 m=4 n\right.$ and $\left.2 k=5 l\right\}$

(iii) $\left\{a^{3^{n}} \mid n \geqslant 0\right\}$

(c) Let $L$ be a CFL. Show that $L^{*}$ is also a CFL.