Question: Problem 3 . Consider the following recursive definition for a set of strings S involving the digits 1 , 2 , 3 : Base Case:

Problem 3. Consider the following recursive definition for a set of strings S involving the digits
1,2,3 :
Base Case: 3inS
Recursive rules: if xinS then so are ,1x2,2x1,s3
A. Write all strings in S of length 4 or less.
B. Prove by induction that the sum of digits for any string in S is divisible by 3.
Problem 3 . Consider the following recursive

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