99 digits of student ID is arbitrary. e.g. 216123789

= 1. Question 1-Regular Expressions Let ni, N2, ..., ng denote the 9 digits of you Student ID. We let {a,b,c} be the alphabet we work with in this question. For each of the languages listed in the parts below, provide description in words or set notation of the language, if the question defines it by a regular expression and provide a regular expression if the question defines the language by a description in words or set notation. For each of the four languages also determine whether the language contains the empty word e and give an example of one word over that is in the language and one such word that is not in the language. Recall that, for a word w, we let |w| denote the length of the word (that is, the number of symbols in w). (a) (ab)* U c(ab)+. (b) 5+09+ U a UbUc (c) {w E * ||w|#n}, where n = n1 + n2 + n3. (d) {w * ||w| is divisible by m}, where m = n1 +na+n4. 2. Question 2Understanding the pumping lemma Let = {a,b,c} and let L1 = {a,b,c, ab, ac} and let L2 be the language from part (d) in Question 1 above. For both L and L2: state whether that language satisfies the pumping lemma and, if possible, state a pumping length p for that language and give an example of a word in the language that is longer than p together with a valid decomposition into parts x, y and z (according to the pumping lemma and your choice of p)