Logic question Given (∀ x)(∃ y)(P(x,y)) I need to provide an example that is true and one that is false. For true Domain is all integers x + y = 0 If y is -x, this is true. False Domain is all real numbers x = y^2 If x = -1, y^2 can never be -1. I think these are ok but unsure. Thank you
Logic question Given (∀ x)(∃ y)(P(x,y)) I need to provide an example that is true and one that is false. For true Domain is all integers x + y = 0 If y is -x, this is true. False Domain is all real numbers x = y^2 If x = -1, y^2 can never be -1. I think these are ok but unsure. Thank you
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
Logic question
Given
(∀ x)(∃ y)(P(x,y))
I need to provide an example that is true and one that is false.
For true
Domain is all integers
x + y = 0
If y is -x, this is true.
False
Domain is all real numbers
x = y^2
If x = -1, y^2 can never be -1.
I think these are ok but unsure. Thank you
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Your examples are correct!
For the true example, if we let the domain be all integers, and P(x,y) is defined as x + y = 0, then we can choose y to be -x for any value of x, and we will have P(x,y) true for all x in the domain.
For example, P(1,-1) is true because 1 + (-1) = 0, and P(2,-2) is also true because 2 + (-2) = 0.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
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)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
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)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
![C How to Program (8th Edition)](https://www.bartleby.com/isbn_cover_images/9780133976892/9780133976892_smallCoverImage.gif)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
![Database Systems: Design, Implementation, & Manag…](https://www.bartleby.com/isbn_cover_images/9781337627900/9781337627900_smallCoverImage.gif)
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education