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2. Proof by contradiction: (a) Let a and b be integers. Show that if a²b -a is even, then a is even or b is odd. (b) Let G be a simple graph on n ≥ 4 vertices. Prove that if the shortest cycle in G has length 4, then G contains at most one vertex of degree n - 1. (c) Let x be a rational number and let y be an irrational number. Show that if x(y rational, then x = 0. -1) is

2. Proof by contradiction: (a) Let a and b be integers. Show that if a²b -a is even, then a is even or b is odd. (b) Let G be a simple graph on n ≥ 4 vertices. Prove that if the shortest cycle in G has length 4, then G contains at most one vertex of degree n - 1. (c) Let x be a rational number and let y be an irrational number. Show that if x(y rational, then x = 0. -1) is

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
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2. Proof by contradiction: (a) Let a and b be integers. Show that if a²b a is even, then a is even or b is odd. (b) Let G be a simple graph on n ≥ 4 vertices. Prove that if the shortest cycle in G has length 4, then G contains at most one vertex of degree n - 1. (c) Let x be a rational number and let y be an irrational number. Show that if x(y − 1) is rational, then x = 0.
Transcribed Image Text:2. Proof by contradiction: (a) Let a and b be integers. Show that if a²b a is even, then a is even or b is odd. (b) Let G be a simple graph on n ≥ 4 vertices. Prove that if the shortest cycle in G has length 4, then G contains at most one vertex of degree n - 1. (c) Let x be a rational number and let y be an irrational number. Show that if x(y − 1) is rational, then x = 0.
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