Question: Consider the language PALINDROME over the alphabet {a b}. (i) Prove that if x is in PALINDROME, then so is x n for any n.

Consider the language PALINDROME over the alphabet {a b}.
(i) Prove that if x is in PALINDROME, then so is xⁿ for any n.
(ii) Prove that if y³ is in PALINDROME, then so is y.
(iii) Prove that if zⁿ is in PALINDROME for some n (greater than 0), then z itself is also.
(iv) Prove that PALINDROME has as many words of length 4 as it does of length 3.
(v) Prove that PALINDROME has as many words of length 2n as it has of length 2n - 1. How many words is that?

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