Let S = {3n : neZ}.A recursive definition for the set S is: Basis Step: 3 ES Recursive Step: If a E S then r +3 E S Prove by structural induction that for every r x € S, x +x E S. Hint: Use the recursive definition of S to set up your proof by structural induction and use the definition S = {3n : n e z*} in your proof.

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