2. (40 points, 8+2 points each) Give a regular expression for the following languages. Explain the expression by writing what each part does. (a) The set of strings over {a,b,c} that contains at least one a and ends in bb. (b) The set of strings over {a,b,c} in which all the a's precede the b's, which in turn precede the c's. It is possible that there are no a's, or b's, or c's and the string is empty. (c) The set of strings over {a,b,c} in which all the a's precede the b's, which in turn precede the c's. It is possible that there are no a's, or b's, or c's, but is not in the language. (d) The set of strings over {1, 2, 3, a} that do not begin with 123. 3. (10 points) The following DFA M1 accepts all strings that end in 'ab'. Give a 5-tuple that formally describes the DFA. Write the transition function as a table. M1: a b >( 90 )