In the following languages, use the pumping lemma to prove that the language is not regular. In
all cases, assuming for contradiction that the language is regular, take $n$ to be the pumping length.
Unless otherwise stated, the alphabet is $\Sigma = \{0, 1\}$.
(a) $L = 0^k 1^k 2^k | n \ge 0$ for the alphabet $\Sigma = \{0, 1, 2\}$.
(b) $L = \{ww | w \in \{0, 1\}^*\}$. Hint: Try the string $0^n 1^n 0^n 1^n$. Can you find a shorter string that also
works?
(c) $L = \{w | w$ is a palindrome, i.e. equal to its reverse}.