Construct RE and FA for the languages of L$1$ L$2($i$.$e$.$ intersection of L$1$ and L$2)$ and $($L$2)*$over S $=\{$a$.$ b$\}$ using Kleene's theorem as exactly discussed in Chapter $7$ of the textbook and the lectures. You will have to start with RE and FA for each language and continue with the steps $($i$.$e$.$ construct RE and FA for each language first and then build an FA for each new language$)$ for the Kleene's theorem for each case.

Write and draw your answers legibly and clearly. Show your working of answers logically$.$