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In: Computer Science

Let M1 = (Q1, Σ, δ1, q1, F1) and M2 = (Q2, Σ, δ2, r1, F2)...

Let M1 = (Q1, Σ, δ1, q1, F1) and M2 = (Q2, Σ, δ2, r1, F2) be DFA's where Q1 = {q1, q2, q3, q4}, F1 = {q1, q3, q4}, Q2 = {r1, r2, r3} and F2 = {r1, r3}. Assume that the cross product construction has been applied to M1 and M2 to produce a new DFA M = (Q, Σ, δ, s0, F), and that all possible states in M are reachable from s0. Please answer the following questions about the set F, the final state set of M.

What is F if M recognizes L(M1) U L(M2)?

What is F if M recognizes L(M1) Intersection L(M2)?
What is F if M recognizes L(M1) - L(M2)?

What is F if M recognizes L(M2) - L(M1)?

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