1) Please answer DFA and NFA for e & f

2) Please answer from Exercise 1.19 problem 1 (d), (e) and (f). That is, draw the state diagrams for each of these languages and also describe the regular expression for each of these languages. For the state diagrams, you only need to draw the state diagram and need not explain it with tables etc. For regular expression, there are many valid representations. I look for the simplest and most elegant expression.

(1) Draw state diagrams for DFA's that realize the following languages. Assume = {0,1}: (a) A = {xx ends with 001}. (b) B = {xlx contains 001}. (c) C = { contains neither 01 nor 10 as substring }. (Hint: think of the complement of this language.) (d) D = {xx has length at least 3 and the third symbol is 0}. (e) E = {x|every odd position of x is 1}. (f) F = { contains even number of I'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