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Suppose the set S is recursively defined as follows: Base step: (1, 1) ∈ S Recursive...

Suppose the set S is recursively defined as follows:

Base step: (1, 1) ∈ S

Recursive step: If (a, b) ∈ S, then (a + 1, b + 2a + 1) ∈ S

3(a). S is the graph of a function. What function is it? What is the function’s domain and range? Rewrite S using set-builder notation. Show your work. (You do not have to prove your answer.)

3(b). Prove that if (a, b) ∈ S, then a + b is even.

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