Determine a regular expression for the language L over the alphabet $\{$a$,$ b$\}$ that ends with a letter that is different from the letter that it starts with. For example, ab$,$ ababab and aaaaabaaaabbbbbb are words in L but aaa, baabbaab, aaaaabaaaaaa and abaa are not. $(2)($b$)$ Design a deterministic finite automaton $($DFA$)$ that will recognise all of the words in as defined above. $(4)($c$)$ Use Theorem $21$ to develop a context$-$free grammar $($CFG$)$ for the language L$.(4)($d$)$ Convert the following CFG to Chomsky Normal Form $($CNF$)$: S bY aZ $|$ aXaY X baY $|$ abZ Y aX $|$ Z bX $|$