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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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Question
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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