(i) When asked to give a recursive definition for the language PA LINDROM E over the alphabet Σ = {a b}, a student wrote:

Rule 1 a and b are in PALINDROME.
Rule 2 If x is in PALINDROME, then so are axa and bxb.
Unfortunately, all the words in the language defined above have an odd length and so it is not all of PALINDROME. Fix this problem.
(ii) Give a recursive definition for the language EVENPALINDROME of all palindromes of even length.