a$.$ Let $\{a,b,c,$dots,$z\}$ be an alphabet. Construct regular expressions for the following languages

i$.$ The set of strings which are zero or more repetitions of the letter $"$a$".$

ii$.$ The set of strings in part $($i$),$ followed by one or more repetitions of strings "aba" or "bab".

iii. The set of strings in part $($ii$),$ followed by one repetition of $"$a$"$ followed by zero or more

repetitions of $"c".$

b$.$ Give three NFAs which accept the set of strings described by the three regular expressions in your

answer to Question $1$a $($i$),($ii$)$ and $($iii$).$

c$.$ Give an example of an NFA that is not a DFA. The NFA should have at least $2$ states and be over

alphabet with at least three letters. Give a brief explanation why the automaton is not a DFA.

d$.$ Give three strings over alphabet $\{x,y\},$ which are recognised by the following regular expression:

$(x|y{)}^{*}(|yy{)}^{+}yyy(yx{)}^{*}$

I NEED YOU TO MAKE PROPER NFA AND DFA DIAGRAMS FOR ME$,$ NOT JUST A CODE. PLEASE I NEED PROPER DIAGRAMS.