Exercise 3.1.1: Write regular expressions for the following languages: * a) The set of strings over alphabet {a,b,c} containing at least one a and at least one b. Exercise 3.1.2: Write regular expressions for the following languages: * a) The set of all strings of 0's and I's such that every pair of adjacent O's appears before any pair of adjacent l's. Exercise 3.2.1: Here is a transition table for a DFA: | 01 91 | 92 91 92 93 91 *93 | 93 | 92 * a) Give all the regular expressions R the state with integer number i. Note: Think of state li as if it were * b) Give all the regular expressions R!). Try to simplify the expressions as much as possible. *e) Construct the transition diagram for the DFA and give a regular expres- sion for its language by eliminating state 02. Exercise 3.2.4: Convert the following regular expressions to NFA's with e- transitions. * a) 01. b) (0+1)01. c) 00(0+1)