Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Then d = "THEOREM": Suppose a, b E N, and d GCD(d, b²). “Proof”": By hypothesis, we have that dla and db, so there are integers s and dt. Then d² = d²s and so d²|a². Similarly, d²|b². Thus d² is a a = ds and b = mon divisor of a and b², as desired.

Then d = "THEOREM": Suppose a, b E N, and d GCD(d, b²). “Proof”": By hypothesis, we have that dla and db, so there are integers s and dt. Then d² = d²s and so d²|a². Similarly, d²|b². Thus d² is a a = ds and b = mon divisor of a and b², as desired.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.2: The Rectangular Coordinate System And Graphing Lines
Problem 103E
See similar textbooks
icon
Related questions
Question
= GCD(a, b). Then d² = GCD(d, b²). e) "THEOREM": Suppose a, b E N, and d "Proof": By hypothesis, we have that dla and db, so there are integers s and I with dt. Then d² = a = ds and b = d'3² and so d²|a². Similarly, d²|b². Thus d² is a com mon divisor of d² and b², as desired.
Transcribed Image Text:= GCD(a, b). Then d² = GCD(d, b²). e) "THEOREM": Suppose a, b E N, and d "Proof": By hypothesis, we have that dla and db, so there are integers s and I with dt. Then d² = a = ds and b = d'3² and so d²|a². Similarly, d²|b². Thus d² is a com mon divisor of d² and b², as desired.
PROOF EVALUATION (This type of exercise will appear occasionally): Each of the follow- ing is a proposed "proof" of a "theorem". However the "theorem" may not be a true statement, and even if it is, the "proof" may not really be a proof. You should read each "theorem" and "proof" carefully and decide and state whether or not the "theorem" is true. Then: G If the "theorem" is false, find where the "proof" fails. (There has to be some error.) . If the "theorem" is true, decide and state whether or not the "proof" is correct. If it is not correct, find where the "proof" fails.
Transcribed Image Text:PROOF EVALUATION (This type of exercise will appear occasionally): Each of the follow- ing is a proposed "proof" of a "theorem". However the "theorem" may not be a true statement, and even if it is, the "proof" may not really be a proof. You should read each "theorem" and "proof" carefully and decide and state whether or not the "theorem" is true. Then: G If the "theorem" is false, find where the "proof" fails. (There has to be some error.) . If the "theorem" is true, decide and state whether or not the "proof" is correct. If it is not correct, find where the "proof" fails.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS