1. (10 points) Consider the DFAs M (on the left) and M (on the right): qo 42 ql b 40 (a) If we use the general constructions discussed in class and in the book for building a DFA whose language is L(M) UL(M) how many states would be in this DFA? Briefly justify your calculation. (b) Draw the state diagram that results from this construction and remove any unreachable states. How many states are left? (c) Describe the language L(M) UL(M) in set builder notation. You may find it useful to first describe L(M) and L(M) in set builder notation first. (d) Use the description from (c) to draw a DFA with fewer states even than what you saw in part (b). Draw the state diagram in JFLAP and include the image in your submission. Note: For parts (b) and (d), you can use the "test equivalence" feature of JFLAP to check your work.