4. Let S be the set of positive integers defined recursively by Basis step: 4 ES Recursive step: x € S - 2x +1 ES No int

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4 Let S Be The Set Of Positive Integers Defined Recursively By Basis Step 4 Es Recursive Step X S 2x 1 Es No Int 1 (15.58 KiB) Viewed 49 times

4. Let S be the set of positive integers defined recursively by Basis step: 4 ES Recursive step: x € S - 2x +1 ES No integers are in S other than those derived from the basis and the recursive steps. (a) [3 points] List the elements of S produced by the first three applications of the recursive rule. Show your work. (6) [5 points] Using structural induction, prove that for every integer x in S. x mod 5 = 4. You should show both the basis step and the inductive step of the proof