Consider the language $L = \{a^i \$ a^j \$ b^k \$ | k ⩽ max(i, j), i, j, k ≥ 0\}$ over the alphabet $\sum = \{a, b, \$ \}$. The complement of the language L, that is, $\sum^* – \text{ L}$ is denoted by $L’$. Which of the following is true?
(a) Both $L$ and $L’$ are regular languages.
(b) $L$ is a context-free language and $L’$ is a regular language.
(c) Both $L$ and $L’$ are context-free languages.
(d) $L$ is a context-free language and $L’$ is not a context-free language.
(e) Neither is $L$ a context-free language nor is $L’$ a context-free language.
