For each of the following languages, give a recursive description of the language. Your basis step must explicitly enumerate a finite number of initial elements. Try to use the shortest description possible (in terms of the number of recursive rules and the number of basis rules). Briefly (1-2 sentences) justify that your description defines the same language but do not give us a full proof; (a) Binary strings that start with 0 and have odd length (i. e. an odd number of characters)
(b) Binary strings r such that len(x) = 1 (mod 3) where len() is the number of characters in r.
(c) Binary strings with an odd number of Os.