Define a set S by 1 ∈ S, and if x, y ∈ S, then x(−y) ∈ S. (a) What is |S|? (b) Prove by structural induction that every

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answerhappygod
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Define a set S by 1 ∈ S, and if x, y ∈ S, then x(−y) ∈ S. (a) What is |S|? (b) Prove by structural induction that every

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Define a set S by 1 ∈ S, and if x, y ∈ S, then x(−y) ∈ S.
(a) What is |S|?
(b) Prove by structural induction that every element of S isodd. (Note, a proof by exhaustion would be quicker, which isunusual for proofs by exhaustion, but I’m asking for a proof usingstructural induction.)
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