$1.(20$ points$)$ Assume $=\{$a$,$ b$\}.$ Answer each of the following questions and explain$/$justify answers with examples considering the following FA$.$ L$1$: All words that end with an a L$2$: All words that begin with an a Prove or disprove that L$1$ L$2$ is a regular language. Use the Kleene$$s theorem to construct the FA and RE if it is regular. Show every step in applying the theorem. Disprove it if it is not regular by using the pumping lemma.