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ow the following propositions using a proof by contradiction. a) Proposition. Suppose n E Z. If n² is odd, then n is odd. ) Proposition. If a, b = Z, then a² - 4b - 20. (Hint: use the proposition that if a² is even, then a is even.) Proposition. There exist no integers a and b for which 18a + 6b = 1.

ow the following propositions using a proof by contradiction. a) Proposition. Suppose n E Z. If n² is odd, then n is odd. ) Proposition. If a, b = Z, then a² - 4b - 20. (Hint: use the proposition that if a² is even, then a is even.) Proposition. There exist no integers a and b for which 18a + 6b = 1.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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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 \( 18a + 6b = 1 \).
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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