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so consider y = 2x, a number m such that y = 3m, then m = 2n? because y = 2(3n). for z = x - y, x = 3n, y=3m, then z = 3n - 3m = 3(n-m). that means k = n-m? is that the right way?

Consider the set S defined recursively as follows: • 3 ∈ S, • if x,y ∈ S,then x−y∈S, • if x∈S, then 2x ∈ S, • S contains no other element. Use Structural Induction to write a detailed, carefully structured proof that ∀ x ∈ S, ∃ n ∈ Z, x = 3n. What I've got is since 3 is in the set...

thanks, it helps a lot

substituting 2n into x? So it becomes (2n) ^2? I don't really get it...

Consider the set T defined recursively as follows: • 2∈T, • if x∈T and x>1,then x/2 ∈T, • if x∈T and x>1,then x^2 ∈T, • T contains no other element. Use Structural Induction to write a detailed, carefully structured proof that ∀ x ∈ T, ∃ n ∈ N, x = 2n. I'm not sure how to...