Define a set S recursively as follows:I. BASE: 0 SII.
Chapter 5, Problem 11E(choose chapter or problem)
Problem 11E
Define a set S recursively as follows:
I. BASE: 0 ∈ S
II. RECURSION: If s ∈ S, then
a. s + 3 ∈ S
b. s − 3 ∈ S
III. RESTRICTION: Nothing is in S other than objects defined in I and II above.
Use structural induction to prove that every integer in S is divisible by 3.
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