Question: Problem 1.10 [10 points] Purpose: Proof of language properties. Read Miscellaneous Exercise 1, page 315 of Kozen's Automata and Computability. Give a formal proof of

Problem 1.10 [10 points] Purpose: Proof of language properties. Read Miscellaneous

Problem 1.10 [10 points] Purpose: Proof of language properties. Read Miscellaneous Exercise 1, page 315 of Kozen's Automata and Computability. Give a formal proof of just the second part Example: Prove that is transitive. Answer: We need to show that . From the annihilator property of on concatenation, we know that = 0. But s by definition, so S. Q.E.D

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