I am asked to find

Prove that the following languages are regular languages:

(a) $\{a^nb^ma^k \mid n\geq3,m\geq1,k\geq1\}$

(b) $\{a^n \mid n\neq3 \text{ and } n\not\equiv2 \mod7\}$

(c) $\{a^nb \mid n\geq2\}\cup\{ab^m \mid m≥3\}$

I have a vague understanding of pumping lemma, and how to prove a language is not regular, but was hoping that someone could walk through (a) with me to give me a better understanding and allow me to do the rest on my own.


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