Use the pumping lemma to demonstrate that $L_1$, $L_2$, $L_3$, $L_4$ and $L_5$ is not regular.
(a) $L_1 = \{w \in \{0, 1\}^* : 0^i 1^j \text{ where } i \le j\}$
(b) $L_2 = \{w \in \{a, b, c\}^* : a^i b^j c^{k+2} \text{ where } i = k \text{ and } i, j, k \ge 0\}$
(c) $L_3 = \{w \in \{0, 1\}^* : w \text{ is a palindrome.}\}$
(d) $L_4 = \{w_1 # w_2 \text{ such that } |w_1| = 2 * |w_2|, \text{ where } \Sigma = \{0, 1\}\}$
(e) $L_5 = \{w \in \{a\}^* : a^{2^n} \text{ where } n \ge 0\}$