State the pumping lemma for context-free languages (CFLs). Which of the following are CFLs? Justify your answers.

(i) $\left\{a^{2 n} b^{3 n} \mid n \geqslant 3\right\}$.

(ii) $\left\{a^{2 n} b^{3 n} c^{5 n} \mid n \geqslant 0\right\}$.

(iii) $\left\{a^{p} \mid p\right.$ is a prime $\}$.

Let $L, M$ be CFLs. Show that $L \cup M$ is also a CFL.