Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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How can we do the proposition for a-c?
MATH 140 - Lecture 12 Homework Name: _________________________ Section: _________________________ 1. Show the following propositions using a proof by contradiction. (a) **Proposition.** Suppose \( n \in \mathbb{Z} \). If \( n^2 \) is odd, then \( n \) is odd. (b) **Proposition.** If \( a, b \in \mathbb{Z} \), then \( a^2 - 4b - 2 \neq 0 \). (Hint: use the proposition that if \( a^2 \) is even, then \( a \) is even.) (c) **Proposition.** There exist no integers \( a \) and \( b \) for which \( 18a + 6b = 1 \).
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Transcribed Image Text:MATH 140 - Lecture 12 Homework Name: _________________________ Section: _________________________ 1. Show the following propositions using a proof by contradiction. (a) **Proposition.** Suppose \( n \in \mathbb{Z} \). If \( n^2 \) is odd, then \( n \) is odd. (b) **Proposition.** If \( a, b \in \mathbb{Z} \), then \( a^2 - 4b - 2 \neq 0 \). (Hint: use the proposition that if \( a^2 \) is even, then \( a \) is even.) (c) **Proposition.** There exist no integers \( a \) and \( b \) for which \( 18a + 6b = 1 \).
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