Complete the following questions concerning the above claim and "proof": (1) Determine whether the “proof" is rigorous. Identify the issues in the "proof", if any. (2) Determine whether the claim is true or false. Justify the answer in part (3). (3) If the the claim is true and the “proof" is not rigorous, then provide a correct and rigorous proof. If the claim is false, give a concrete counterexample. Hint. Complete the parts as instructed. If the claim is false, then (obviously) there is no way the “proof" could be correct.
Complete the following questions concerning the above claim and "proof": (1) Determine whether the “proof" is rigorous. Identify the issues in the "proof", if any. (2) Determine whether the claim is true or false. Justify the answer in part (3). (3) If the the claim is true and the “proof" is not rigorous, then provide a correct and rigorous proof. If the claim is false, give a concrete counterexample. Hint. Complete the parts as instructed. If the claim is false, then (obviously) there is no way the “proof" could be correct.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 2E
Related questions
Question
Transcribed Image Text:Problem 4.4 (Grade a "Proof"). Study the following claim as well as the "proof":
Claim. For all sets A, B and C, if ACBUC then P(A) C P(B)U P(C).
"Proof". Let A, B and C be sets. Assume A CBUC. Let x be an arbitrary
element and suppose r € P(A). Note that r E P(A) implies r E A. Then, since
ACBUC, we get r e BUC, which then implies x e B or x € C. Therefore, we
see r € P(B) or x € P(C), which simply means r E P(B)U P(C). Since every
x in P(A) must be in P(B) U P(C), we conclude P(A) C P(B)U P(C).
Complete the following questions concerning the above claim and "proof":
(1) Determine whether the "proof" is rigorous. Identify the issues in the "proof",
if any.
(2) Determine whether the claim is true or false. Justify the answer in part (3).
(3) If the the claim is true and the "proof" is not rigorous, then provide a correct and
rigorous proof. If the claim is false, give a concrete counterexample.
Hint. Complete the parts as instructed. If the claim is false, then (obviously) there is no
way the "proof" could be correct.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning