1. Write \graf code for a DFA M_1 that recognizes the @lang of strings over \S={a,b} such that >> L(M_1)={w:|{w} is a multiple of 3}.

2. Write \graf code for a DFA M_2 that recognizes the @lang of strings over \S={a,b} such that >> L(M_1)={w:|{w} is even}.

3. Use the !{process from class} to write \graf code for a DFA M_3 such that L(M_3)=L(M_1)\uL(M_2).

4. Modify the process from class to write \graf code for a DFA M_4 such that L(M_4)=L(M_1) L(M_2). What did you change about the process? Why does that work in general?

5. Describe L(M_4) using set builder notation.

6. Describe ~{L(M_3)} using set builder notation.

7. Write \graf code for a DFA M_5 that recognizes ~{L(M_3)}. How would you recognize the complement of the @lang recognized by a DFA in a generalized process? What makes your process work?

8. Use the \graf Simulator to show 2 strings that are accepted by M_5.