3. Hope Strings Eternal (20 points) For each of the following, write a recursive definition of the sets satisfying the following properties. Briefly justify that your solution is correct. (a) [5 Points] Binary strings with length divisible by 3 (b) [5 Points Binary strings where every occurrence of a 0 is immediately followed by a 1 (c) [5 Points] Binary strings that start with 1 and have even length (d) [5 Points] Binary strings with an odd number of 1s