Question: 1. Prove that [] $. (Hint: the forward direction is immediate. For the converse, consider using the empty string for in the definition of ~.)

1. Prove that [] $. (Hint: the forward direction is immediate. For the converse, consider using the empty string for in the definition of ~.) 2. Prove that : ([],) = [(,)]. Induct on the length of . 3. Prove that () = (). Use the results of the last two parts in your proof. 4. Why cant be further reduced by repeating the process?

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