3. Let L = {we {0,1}* : w contains at least one 1}, and let A...

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3. Let L = {we {0,1}* : w contains at least one 1}, and let A be the DFA with tabular represen- tation: A || 0 1 P q * 9 q q Prove that LL(A). Hint: Do the L(A) L part of the proof by induction on the the length of the string processed by A. You need a mutual induction with a claim for state p and a claim for state q. Then use the contrapositive L(A) L to show that L L(A). 3. Let L = {we {0,1}* : w contains at least one 1}, and let A be the DFA with tabular represen- tation: A || 0 1 P q * 9 q q Prove that LL(A). Hint: Do the L(A) L part of the proof by induction on the the length of the string processed by A. You need a mutual induction with a claim for state p and a claim for state q. Then use the contrapositive L(A) L to show that L L(A).