Question 1 Give a regular expression over the alphabet ={a,b} for the set of words in which the substring ' ab ' does not occur. For example, "baa" will be accepted but "aab" will not. [2 marks] Question 2 Consider the regular expression (ab)a. In a step-by-step fashion, using the rules from Handout 2b, convert each sub-expression of the regular expression into an ENFA and, by doing so, obtain a DFA that is equivalent to the overall regular expression. [5 marks] Question 3 Consider the following sequence of natural numbers D=(0,1,2,3,6,11,20,) defined as D(0)=0, D(1)=1,D(2)=2 and D(n+3)=D(n)+D(n+1)+D(n+2). Show, by induction, that for any natural number n,D(n)