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.proof 2 only ign Window HelpSQUIZ NO 1. Metho... x#ITUUTT Suppose that u and are both oud mogels. Then there Carst imegus, A2b) "Proof 2": Suppose that a b is even and a is odd. Then there exist integers k₁, k2 suchthat a - b = 2k₁ and a = 2k₂ + 1. Thusb=b_a+a-2k₁ + 2k2 +1 = 2(k₂ − k₁) + 1so b is odd, a contradiction.8.50 x 14.00 in1/2such that a 2k₁ + 1 and b 2k₂ + 1. Thus, a – b = 2k₁ + 1 − (2k₂ + 1) = 2(k₁ – kwhich is even.Type here to searchc) "Proof 3": Suppose that a - b is odd. Then there exist an integer k₁ such that a - b = 2k₁ + 1.If b is even we are finished, so suppose that b is odd, say b2k2+1 for someinteger k Thus ab+b=2k + 1 (2k +1)=2(k₁k₂)so a is even andTl==

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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. proof 2 only

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. proof 2 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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Assume x and y are two odd numbers and x/y is an integer. Which of the following statements are true? X + y is odd Xy is odd X/y is odd X-y is odd
1d and 1e