Discrete math problem

Let B (0.1). The following is a recursive definition for B, the set of all binary strings of length 0 or larger. Recall that ? is the symbol for the empty string that has no characters. ???'. If z E B., then z0 e B. and zl E B. Give a recursive definition for the set S which is all binary strings in which all the O's come before all the 1's. For example 0011111 S, but 0010111 s. Recursively define the sets of all positive integers as described. Identify the basis and the algorithm. Denote D- (0, 1, 2, 3, 4,5,6,7,8,9. 1. All numbers with digits from (1, 2, 3). 2. All numbers without digits from (0, 2, 4, 6, 8). 3. All numbers with no 7. 4. All mumbers with only 7 Let B (0.1). The following is a recursive definition for B, the set of all binary strings of length 0 or larger. Recall that ? is the symbol for the empty string that has no characters. ???'. If z E B., then z0 e B. and zl E B. Give a recursive definition for the set S which is all binary strings in which all the O's come before all the 1's. For example 0011111 S, but 0010111 s. Recursively define the sets of all positive integers as described. Identify the basis and the algorithm. Denote D- (0, 1, 2, 3, 4,5,6,7,8,9. 1. All numbers with digits from (1, 2, 3). 2. All numbers without digits from (0, 2, 4, 6, 8). 3. All numbers with no 7. 4. All mumbers with only 7