Define the set S by
Basis step: 2 ∈ S, 5 ∈ S
Recursive step: if a,b ∈ S then (a+2b)/3 ∈ S
a) List all elements of S generated by the 1st, 2nd, and 3rd application of the recursive step.
b) Use structural induction to prove 2 ≤ c ≤ 5 for all c ∈ S.
c) Give a non-recursive formula for S
d) Prove the formula in part c) is correct.
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