Exercise 1.19 from notes, do 1) e, f and 2) e, f. Exercise 1.19. (1) Draw state diagrams for DFA's that realize the following languages. Assume E = {0,1}: (a) A = {x|x ends with 001}. (b) B = {x|x contains 001}. (c) C = {x|x contains neither 01 nor 10 as substring }. (Hint: think of the complement of this language.) (d) D= {x|x has length at least 3 and the third symbol is (}. (e) E = {x|every odd position of x is 1}. (f) F = {x|x contains even number of O's }. Describe each of the above languages using regular expressions. (2) For each of the above languages, draw the simplest state diagram of an NFA that realizes it. For Problem 2 e) and f), some of you may be wondering, since every DFA is also NFA, what is there to show? The key phrase in the problem is simplest possible state diagram", meaning using the fewest required states. NFA can be drawn with significantly fewer states than the associated DFA, in most cases. I am looking for the fewest required states for the NFA. Your solutions for these problems could imply be the drawings of the state diagrams and a very brief explanation of why they are correct