A language called PALINDROME is defined over the alphabet . = {a, b}: PALINDROME = {, and all strings x suth that reverse(x) = x}

When asked to give a recursive definition for the language PALINDROME, 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. (a) Change Rule 1 (Rule 2 should not change) such that the recursive definition defines the language PALINDROME. (b) Change Rule 2 (Rule 1 should not change) such that the recursive definition defines the language PALINDROME. (c) Give a recursive definition for the language containing only even-length PALINDROME strings. (d) How many words does the language PALINDROME have of length 3? (e) How many words does the language PALINDROME have of length 4?