Question

Let s be the subset of the set of ordered pairs of integers defined recursively by basis step: (0, 0) ∈ s. 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.

Answer 1

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