Let N = {0, 1, 2, 3, . . .}. Let 𝑆 be the subset of N × N defined as follows: (i) (0, 0) ∈ 𝑆. (ii) If (&

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Let N = {0, 1, 2, 3, . . .}. Let 𝑆 be the subset of N × N
defined as follows:
(i) (0, 0) ∈ 𝑆.
(ii) If (𝑚, 𝑛) ∈ 𝑆, then (𝑚, 𝑛 + 1) ∈ 𝑆, (𝑚 + 1, 𝑛 + 1) ∈ 𝑆, and
(𝑚 + 2, 𝑛 + 1) ∈ 𝑆.
(a) List nine elements of 𝑆 following (0, 0).
(b) True or false: if (𝑚, 𝑛) ∈ 𝑆 then 𝑚 ≤ 2𝑛. Prove your
answer