12. A palindrome over an alphabet ? is a string in ?. that is spelled the same forward and backward. The set of palindromes over 2 can be defined recursively as follows: i) Basis: ? and a, for all a ?, are palindromes. ii) Recursive step: If w is a palindrome and E ?, then awa is a palindrome. ii) Closure: w is a palindrome only if it can be obtained from the basis elements by a finite number of applications of the recursive step. Prove that these two The set of palindromes can also be defined by {w | w definitions generate the same set