Question

(b) Let S be the set of positive integers defined recursively as follows: Basis step: 1 ? S. Recursive step: if n ? S, then 3n + 2 ? S and n² ? S. Show that (i) if n ? S, then n ? 1 (mod 4), and (ii) there exists a positive integer m ? 1 (mod 4) such that m ? S.

          (b) Let S be the set of positive integers defined recursively as follows:
Basis step: 1 ? S.
Recursive step: if n ? S, then 3n + 2 ? S and n² ? S.
Show that (i) if n ? S, then n ? 1 (mod 4), and
(ii) there exists a positive integer m ? 1 (mod 4) such that m ? S.

(b) Let S be the set of positive integers defined recursively as follows:
Basis step: 1 ? S.
Recursive step: if n ? S, then 3n + 2 ? S and n² ? S.
Show that (i) if n ? S, then n ? 1 (mod 4), and
(ii) there exists a positive integer m ? 1 (mod 4) such that m ? S.

Added by Robert M.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Adi S

06/16/2022

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(b) Let S be the set of positive integers defined recursively as follows: Basis step: 1 ∈ S. Recursive step: if n ∈ S, then 3n + 2 ∈ S and n² ∈ S. Show that (i) if n ∈ S, then n ≡ 1 (mod 4), and (ii) there exists a positive integer m ≡ 1 (mod 4) such that m ∉ S.