1. Let A be the set of palindromes over fa, by Suppose you are trying to prove that A is not regular using the pumping lemma. Your proof starts (correctly) like this Suppose for a contradiction that A is regular. Let p be the pumping length given by the pumping lemma Now you have to choose string s. For each choice of s below, you have to state whether or not this choice of s can be used to finish the proof that A is not regular. If you answer that s can not be used, you should also briefly and clearly explain why it can not be used. If you answer that s can be used, you do not have explain anything (a) s-b'a"b. Can this s be used? yes / no If you said no, briefly explain your answer. b) s-aP. Can this s be used? yes / no. If you said no, briefly explain your answer (c) s- aPb. Can this s be used? yes / no. If you said no, briefly explain your answer. (d) s -af-1baf-1. Can this s be used? yes / no If you said no, briefly explain your answer. (e) s- aaabbaaa. Can this s be used? yes / no. If you said no, briefly explain your answer. (f) s-(ab)Pa. Can this s be used? yes / no If you said no, briefly explain your answer. (g) s-aPbaP. Can this s be used? yes / no. If you said no, briefly explain your