Determine which of the following “proofs” are correct and which are incorrect. If a proof is correct, indicate the type and if a proof is incorrect, indicate why it is incorrect.Theorem: If a and b are even integers then a – b is an even integer.Letter g and First picture only. "Proof 10: Suppose a and bare odd and a – b is odd. Then there exist integers k₁, k₂ such thata=2k₁ + 1, b = 2k₂ + 1. Thus we have a - b = 2k₁ +1 − (2k₂ + 1) = 2(k₁ −k₂)so a-b is both odd and even, a contradiction.V2of 2GQ and we are finishedg) “Proof 7¹: Suppose that a and b are both even. Then there exist integers k₁, k₂ such thata = 2k₁ and b = 2k₂. Thus, a – b = 2k₁ – 2k₂ = 2(k −k₂) so a - b is even.h) "Proof 8: Suppose that a – b is even. Then if a is odd we are done, so suppose that a isThen there exist integers kỵ, k² such that a − b = 2k₁ and a = 2k₂. Thus,b=a_(a−b) = 2k₂ - 2k, = 2(kk) so b is also even.

Answered: Image /qna-images/answer/29ab6724-d41e-49c7-97b2-9776aeba6569.jpg

Determine which of the following “proofs” are correct and which are incorrect. If a proof is correct, indicate the type and if a proof is incorrect, indicate why it is incorrect.Theorem: If a and b are even integers then a – b is an even integer. Letter g and First picture only.

Determine which of the following “proofs” are correct and which are incorrect. If a proof is correct, indicate the type and if a proof is incorrect, indicate why it is incorrect.Theorem: If a and b are even integers then a – b is an even integer. Letter g and First picture only.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Instructions: Determine which of the following “proofs” are correct and which are incorrect. If a proof is correct, indicate the type and if a proof is incorrect, indicate why it is incorrect. Write your answer inside the box. Theorem: If a and b are even integers then a – b is an even integer.
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