a. Let {a,b,c,,z} be an alphabet. Construct regular expressions for the following languages i. The set of words which are zero or more repetitions of the letter " a ". ii. The set of words in part (i), followed by one or more repetitions of words "aba" or "bab". iii. The set of words in part (ii), followed by one repetition of " a " followed by zero or more repetitions of "c". [6 marks] b. Give three NFA which accept the set of words described by the three regular expressions in your answer to Question 1a (i), (ii) and (iii). [7 marks] c. Give an example of a nondeterministic finite automaton (NFA) that is not a deterministic finite automaton (DFA). The NFA should have at least four states and be over alphabet with at least three letters. Give a brief explanation why the automaton is not a DFA. [6 marks] d. Give three words over alphabet {x,y,z}, which are recognised by the following regular expression: (xy)(xxyy)+yyy(yx)