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(1) What is the valve (2) to show Use integars that if w/ ab - 0 then. of the axioms for integers for a and b are b=0 - a=0 2 av

(1) What is the valve (2) to show Use integars that if w/ ab - 0 then. of the axioms for integers for a and b are b=0 - a=0 2 av

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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Examples using the properties 1. Suppose that a, b and c are integers w/ a <b and c> 0, show that ac < bc Proof. By definition of a<b, we have b-a > 0. By closure property, c(b-a) >0. By distributive law, c( b-a) = bc - ac. Thus we have, bc- ac > 0 or ac- bc <0 as desired. Sample Bolutions i need like this please 2. Show that 0.a = 0, a Z Proof. Let 0+0 = 0 This holds since 0 is an identity element for addition. Multiply both sides by a, so we get (0+0)a=0.a By distributive law, we have (0+0)a= 0.a +0.a = 0.a Subtract from both sides 0.a, we have (0.a + 0.a) - 0.a = 0.a -0.a By associative law, we get 0.a + (0.a- 0.a) = 0.a + 0 = 0.a The right hand side becomes 0.a - 0.a = 0, Thus we get 0.a = 0
Transcribed Image Text:Examples using the properties 1. Suppose that a, b and c are integers w/ a <b and c> 0, show that ac < bc Proof. By definition of a<b, we have b-a > 0. By closure property, c(b-a) >0. By distributive law, c( b-a) = bc - ac. Thus we have, bc- ac > 0 or ac- bc <0 as desired. Sample Bolutions i need like this please 2. Show that 0.a = 0, a Z Proof. Let 0+0 = 0 This holds since 0 is an identity element for addition. Multiply both sides by a, so we get (0+0)a=0.a By distributive law, we have (0+0)a= 0.a +0.a = 0.a Subtract from both sides 0.a, we have (0.a + 0.a) - 0.a = 0.a -0.a By associative law, we get 0.a + (0.a- 0.a) = 0.a + 0 = 0.a The right hand side becomes 0.a - 0.a = 0, Thus we get 0.a = 0
formative (1) What is the valve (2) to show Use integers assesment. that if using the axioms for integers a and b are w/ ab=0 then Show positive provide that b = 0 of integers of -0? there a=0 is no integer less than 1 OV proof For answers fundametal properties
Transcribed Image Text:formative (1) What is the valve (2) to show Use integers assesment. that if using the axioms for integers a and b are w/ ab=0 then Show positive provide that b = 0 of integers of -0? there a=0 is no integer less than 1 OV proof For answers fundametal properties
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