1. Question 1-Languages, DFAs and NFAs Let ni, n2, ..., ng denote the 9 digits of you Student ID. We let S = {0,1,2,3,4,5,6,7,8,9} be the alphabet of digits. Your student ID and any (substring of it) is a word over this alphabet. We define the following languages: A = {nn2 ... ng} B = {w w is a student ID of some student in this class} The language A contains only one word, namely your student ID. The languages B contains 150 words,namely all student IDs of students in this class. Note that all student IDs of students enrolled in this class have the prefix '21'. (a) Is your student ID accepted by the following NFA? Explain why or why not: 2 6,7,8 0,1,3,6,7 5 91 42 93 94 (b) Show that A is a regular language. (c) Design a DFA that accepts all 9-digit words over that have the prefix '21'. That is, all student IDs in this class should be accepted by that DFA. (You may provide a state diagram or a formal description). (d) Describe how to design an automaton (NFA or DFA) that will accept all the student IDs in this class, except yours. (e) Identify the language that the NFA from part (a) recognizes