Q1) Consider the language S*, where S = {a ab ba). Is the string (abbba) a word in this language? Write out all the words in this language with six or fewer letters. What is another way in which to describe the words in this language? Be careful, this is not simply the language of all words without bbb 10 Points Q2) Let (a, bh a) Consider the language S*, where S= {aa ab ba bb). Give another description of this language b) Give an example of a set S such that S* only contains all possible strings of a's and b's that have length divisible by 10 Points Q3) Let = {a, b). Give recursive definitions for the following languages over a) The language BB of all words containing the substring b) The language NOTBB of all words not containing the substring bb Q4) Let = {a, b). Construct a regular expression defining each of the following languages over. a) The language of all words that do not begin with ba. b) The language of all words in which the total number of 10 Points b's is divisible by 3 no matter how they are distributed, 10 Points such as bbabbaabab. Q5) Show (by giving a brief explanation) that the following pairs of regular expressions define the same language over the alphabet = {a, b} a) b*(ab and (b*a)*b* b) b*(aaab and (b*aaa)*b 10 Points