Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically equivalent to T. (619)]19
Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically equivalent to T. (619)]19
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
Please help me with this. I am having trouble understanding what
![Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically
equivalent to T.
[p^ (p→q)] →q
(pvq) v q by De Morgan's law
pv (q v q) by associative law
(p^q) →q=(pq) v q by logical equivalence
(p ^ q) →q by identity law
(p^ q) →q=[-p v (p→q)] v q by logical
equivalence
[pA (p→q)] → q
[p^ (p→q)] →q = [p^ (pv q)] →q by logical
equivalence
T by domination law
pv (qv q) by associative law
[F v (p ^ q)] →→q by negation law
[(p v p) ^ (pvq)] v q by distributive law](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F247d8035-87d8-4c44-a5de-dbb3e4e84ee6%2Fcc29ecd7-d02e-416f-a33b-327d9da0ef2b%2Fjwbnhgo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove the given expression is a tautology by developing a series of logical equivalence to demonstrate that it is logically
equivalent to T.
[p^ (p→q)] →q
(pvq) v q by De Morgan's law
pv (q v q) by associative law
(p^q) →q=(pq) v q by logical equivalence
(p ^ q) →q by identity law
(p^ q) →q=[-p v (p→q)] v q by logical
equivalence
[pA (p→q)] → q
[p^ (p→q)] →q = [p^ (pv q)] →q by logical
equivalence
T by domination law
pv (qv q) by associative law
[F v (p ^ q)] →→q by negation law
[(p v p) ^ (pvq)] v q by distributive law
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 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education