1. (22 points) (a) Let E = a0" + b0 be a regular expression over = {a, b, 0.1). Which of the following is a string in L(E): (circle all that are correct) (a) a0* (b) e (c) aa00 (d) (e) b (f) none of those choices (b) A student ID number is an 8-digit number. There is a DFA M such that L(M) = {ID numbers of currently registered students at UVic) which will en- able the university to check if an ID number belongs to some student using 8 steps in the DFA T F (c) A student password is made up of letters and numbers and has arbitrary length. There is a DFA M which can check if a student has entered a password, followed by a carriage return, followed by a repeat of the same password using 2*(length of the password) +1 transitions T F (d) Let M be an NFA. When M receives w as input, if there is a computation path which does not end in an accept state then this implies w L(M) T F (e) If A and B are regular languages, then the language PS = {wu I w is a prefix of A and u is a suffix of B} is always regular. T F (f) Every subset of a regular language is a regular language T F