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6. Use the algorithm from class to write Grafstate code for a DFA called \( M \) that recognizes the language \( L\left(M_{1}\right) \cup L\left(M_{2}\right) \). 7. Describe the language recognized by M. 8. Does your machine have any states that are not necessary? If so, then identify them. A state is not necessary if the state does not contribute to the computation of any string 9. Considering the logical purpose of the states used \( M_{1} \) and \( M_{2} \), explain why the states identified in problem 8 are not necessary and why the Union algorithm produced them. 10. Modify your Grafstate code from problem 8 to produce an equivalent DFA that does not have any states that are not necessary. Two DFAs \( M_{1} \) and \( M_{2} \) are said yo be equivalent (written \( \left.M_{1} \cong M_{2}\right) \) if \( L\left(M_{1}\right)=L\left(M_{2}\right) \).