a$)$ Give a possible regular expression that generates the language $L$ consisting of all words in which all words

either contain no $a^{\text{'}}$ s at all, or

when there are $a^{\text{'}}s,$ they occur in clumps of three or more $a^{\text{'}}s,$ and

when there are $a^{\text{'}}s,$ there are an even number of such clumps of $a^{\text{'}}s.$

For instance, words such as $b,$bbbbbaaaabaaaaabbb and aaabbbaaaaaabaaabaaab are words in this language, and words such as aaaa and aaabaa are not words in the language.

b$)$ Construct a regular expression that defines the language $L$ containing all words with at least one aab$-$substring or all words with at least one $ba-$substring.