$19.$ Give recursive definitions for the following languages over the alphabet

$\{$a$,$b$\}$:

$($i$)$ The language EVENSTRING of all words of even length.

$($ii$)$ The language ODDSTRING of all words of odd length.

$($iii$)$ The language AA of all words containing the substring aa$.$

$($iv$)$ The language NOTAA of all words not containing the substring aa$.$