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Applications of the recursive step

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Reference no: EM131570714

Question: Let S be the subset of the set of ordered pairs of integers defined recursively by

Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S and (a + 3, b + 2) ∈ S.

a) List the elements of S produced by the first five applications of the recursive definition.

b) Use strong induction on the number of applications of the recursive step of the definition to show that 5 | a + b when (a, b) ∈ S.

c) Use structural induction to show that 5 | a + b when (a, b) ∈ S.

Reference no: EM131570714

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