Let S = {3n : n e Z}. A recursive definition for the set S is: Basis Step: 3 ES Recursive Step: If x ES then x +3 E S Prove by structural induction that for every x E 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 € Z*} in your proof. %3D

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Chapter2: Second-order Linear Odes
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Let S = {3n : nEZ*}.A recursive definition for the set S is:
Basis Step: 3ES
Recursive Step: If x E S then x +3 E S
Prove by structural induction that for every x E 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 eZ} in your proof.
Transcribed Image Text:Let S = {3n : nEZ*}.A recursive definition for the set S is: Basis Step: 3ES Recursive Step: If x E S then x +3 E S Prove by structural induction that for every x E 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 eZ} in your proof.
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