Define a set S recursively as follows:I. BASE: 0 S, 5 SII.
Chapter 5, Problem 10E(choose chapter or problem)
Problem 10E
Define a set S recursively as follows:
I. BASE: 0 ∈ S, 5 ∈ S
II. RECURSION: If s ∈ S and t ∈ S then
a. s + t ∈ S
b. s − t ∈ 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 5.
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