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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
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. proof 2 only
ign Window Help S QUIZ NO 1. Metho... x # ITUUTT Suppose that u and are both oud mogels. Then there Carst imegus, A2 b) "Proof 2": Suppose that a b is even and a is odd. Then there exist integers k₁, k2 such that a - b = 2k₁ and a = 2k₂ + 1. Thus b=b_a+a -2k₁ + 2k2 +1 = 2(k₂ − k₁) + 1 so b is odd, a contradiction. 8.50 x 14.00 in 1/2 such that a 2k₁ + 1 and b 2k₂ + 1. Thus, a – b = 2k₁ + 1 − (2k₂ + 1) = 2(k₁ – k which is even. Type here to search c) "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 b 2k2+1 for some integer k Thus a b+b=2k + 1 (2k +1)=2(k₁k₂) so a is even and T l = =
Transcribed Image Text:ign Window Help S QUIZ NO 1. Metho... x # ITUUTT Suppose that u and are both oud mogels. Then there Carst imegus, A2 b) "Proof 2": Suppose that a b is even and a is odd. Then there exist integers k₁, k2 such that a - b = 2k₁ and a = 2k₂ + 1. Thus b=b_a+a -2k₁ + 2k2 +1 = 2(k₂ − k₁) + 1 so b is odd, a contradiction. 8.50 x 14.00 in 1/2 such that a 2k₁ + 1 and b 2k₂ + 1. Thus, a – b = 2k₁ + 1 − (2k₂ + 1) = 2(k₁ – k which is even. Type here to search c) "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 b 2k2+1 for some integer k Thus a b+b=2k + 1 (2k +1)=2(k₁k₂) so a is even and T l = =
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