(10 pts.) Let M = (Q, , ,A, ) be an NFA. Which of the following, if any, would be a correct substitute for the second part of the definition of "? Either prove that it is correct, or explain why it is incorrect A(* (r,y)) whenever a E , y E *, q E rEA(5(q,a)) * (r,y)) whenever a E ' y E *, q E Tip: Pick a small example of an NFA and try to see what these definitions give for . Do they even define * properly? Remember that intuitively * means all the states we can reach by combining A-transitions with moves corresponding to symbols in the input. Do these definitions allow for such freedom? If not, try to come up with a counterexample. Otherwise try to prove that they give the same result. Note: If you have a counterexample, it should be specific (try to make it as small as possible), and you should compute a specific value of * using both the definition given and our definition to see that they are different. (10 pts.) Let M = (Q, , ,A, ) be an NFA. Which of the following, if any, would be a correct substitute for the second part of the definition of "? Either prove that it is correct, or explain why it is incorrect A(* (r,y)) whenever a E , y E *, q E rEA(5(q,a)) * (r,y)) whenever a E ' y E *, q E Tip: Pick a small example of an NFA and try to see what these definitions give for . Do they even define * properly? Remember that intuitively * means all the states we can reach by combining A-transitions with moves corresponding to symbols in the input. Do these definitions allow for such freedom? If not, try to come up with a counterexample. Otherwise try to prove that they give the same result. Note: If you have a counterexample, it should be specific (try to make it as small as possible), and you should compute a specific value of * using both the definition given and our definition to see that they are different