discrete math. Structural Induction: Please write and explain clearly. Thank you.
SOLUTION
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step...
4. (10pts) Let S be the subset of the set of binary strings defined recursively by Basis: XES. Recursive rule: If ze S, then c0 € S, and 1.6 ES. List the elements of S produced by the recursive definition with length less than or equal to 3.
Suppose that the following subset T of binary strings is defined recursively: • Basis: 1 is in T • Recursively, if the binary string s is in T, then so are the strings Os, so, 181, 11s and s11 1. Carefully show why the string 011001 must be in the set T. 2. Provide an argument that shows that if s is a string in T of length n and s has an odd number of 1s, then all strings...
8. Let D be the set whose members are defined as follows. Basis Step: the number 3ED Recursive Step: if x E D and y e D, then x + y e D. Prove that D={3n:n e +}.