Question: Define, recursively, the set S: 1. 3 S 2. if n S, then 4n + 2 S if n S, then 3n 2 2 S

Define, recursively, the set S:

1. 3 S

2. if n S, then 4n + 2 S

if n S, then 3n2 2 S

Prove, using structural induction, that for n S, k Z, k 0, so that n = 11k + 3 (i.e., n 3 (mod 11)).

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