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9 - K) = 1, Which is impoSsible. Which proof method is used in above proof. Proof by counterexample O Direct proof Proof by contraposition Proof by contradiction

9 - K) = 1, Which is impoSsible. Which proof method is used in above proof. Proof by counterexample O Direct proof Proof by contraposition Proof by contradiction

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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Consider the following proof that if x and y are two even integers, then their sum is even. Proof: Assume that x and y are two even integers but their sum is not even, then x + y is odd. By definition, there are some integers p, q, and k such that x = 2p, y = 2q, and x + y = 2k + 1. Therefore, 2k + 1 = x + y = 2p + 2q. Rewrite above equation, we have 2(p + q - k) = 1, which is impossible. Which proof method is used in above proof. O Proof by counterexample Direct proof Proof by contraposition O Proof by contradiction
Transcribed Image Text:Consider the following proof that if x and y are two even integers, then their sum is even. Proof: Assume that x and y are two even integers but their sum is not even, then x + y is odd. By definition, there are some integers p, q, and k such that x = 2p, y = 2q, and x + y = 2k + 1. Therefore, 2k + 1 = x + y = 2p + 2q. Rewrite above equation, we have 2(p + q - k) = 1, which is impossible. Which proof method is used in above proof. O Proof by counterexample Direct proof Proof by contraposition O Proof by contradiction
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