3. (10 points) Consider the DFA, M, whose state diagram is given by: q2 0 q1 q3 a. True or False Any string which has a nonempty prefix accepted by this DFA is also accepted by the b. True or False There is a positive integer n such that all strings of length n are in L(M). Recall c. Give a regular expression R so that L(R) is an infinite subset of the language of this DFA. If L(R)S DFA. Briefly justify your answer. "positive" means strictly positive, n > 0. Briefly justify your answer L(M), give an example string that is accepted by M but which is not in L(R). If L(R) L(M), briefly justify the set equality. Note: there are many correct answers for this question. 3. (10 points) Consider the DFA, M, whose state diagram is given by: q2 0 q1 q3 a. True or False Any string which has a nonempty prefix accepted by this DFA is also accepted by the b. True or False There is a positive integer n such that all strings of length n are in L(M). Recall c. Give a regular expression R so that L(R) is an infinite subset of the language of this DFA. If L(R)S DFA. Briefly justify your answer. "positive" means strictly positive, n > 0. Briefly justify your answer L(M), give an example string that is accepted by M but which is not in L(R). If L(R) L(M), briefly justify the set equality. Note: there are many correct answers for this