Give recursive definitions (basis and recursive step) for each of the following sets: (a) The set of positive numbers that are integer powers of 3. (The exponent can be a positive integer, a negative integer, or zero.) (b) The set of binary strings with an equal number of 0's and 1's, where all 0's precede all 1's (e.g., lambda, 01,0011,000111, etc.). Here lambda denotes the empty string. (c) The set of binary strings that are palindromes, i.e., read the same left-to-right and right-to-left (e.g., lambda, 0, 1, 11011, 0110, etc.)