Section: Date: ons: Determine which of the following "proofs" are correct and which are incorrect. If a proof dicate the type and if a proof is incorrect, indicate why it is incorrect. Write your answer insic trictly no erasures. Theorem: If a and b are even integers then a - b is an even integer. roof 1: Suppose that a and b are both odd integers. Then there exist integers k₁, k₂ such that a 2k₁ + 1 and b 2k2 + 1. Thus, a − b = 2k₁ + 1 − (2k2 + 1) = 2(k₁ −k2, which is even. -

Section: Date: ons: Determine which of the following "proofs" are correct and which are incorrect. If a proof dicate the type and if a proof is incorrect, indicate why it is incorrect. Write your answer insic trictly no erasures. Theorem: If a and b are even integers then a - b is an even integer. roof 1: Suppose that a and b are both odd integers. Then there exist integers k₁, k₂ such that a 2k₁ + 1 and b 2k2 + 1. Thus, a − b = 2k₁ + 1 − (2k2 + 1) = 2(k₁ −k2, which is even. -

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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Question

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.

TECH
Proof.pdf - Adobe Acrobat Rea
Vindow Help
QUIZ NO 1. Metho... x
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↓
W
1 / 2
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Section:
Date:
ons: Determine which of the following "proofs" are correct and which are incorrect. If a proof
dicate the type and if a proof is incorrect, indicate why it is incorrect. Write your answer insid-
trictly no erasures.
Theorem: If a and b are even integers then a – b is an even integer.
'roof 1'': Suppose that a and b are both odd integers. Then there exist integers k₁, k₂
such that a 2k₁ + 1 and b − 2k₂ + 1. Thus, a − b − 2k₁ + 1 − (2k2 + 1) = 2(k₁ − K2)
which is even.

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