4. Recall that Definition 1. Parallel Lines Two lines 1₁ and 12 are called parallel if they don't intersect with each other. (a) Discuss the 3-points model we explained in the lecture. Show that there are no parallel lines in this model. (b) Generalise the 3-points model to 4-points model, by giving the inter- pretation to primitive terms and verifying axioms. (c) Are there parallel lines in the 4-points model?

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
icon
Related questions
Question
100%

How do you solve this question? We will use Hilbert’s axiom system that is constructed with the three primitive terms point, line and plane (lie on). An example of giving the interpretation to primitive terms is given in the second photo

1. S²
Consider the S² Geometry, whose interpretation is the following:
point: Point on the surface of the unit sphere
S² = {(x, y, z) € R³|x² + y² + z² = 1}.
● line: The great circles¹ of the unit sphere.
● lie on: A point p = (x, y, z) = S² lies on a great circle l if p = l.
Transcribed Image Text:1. S² Consider the S² Geometry, whose interpretation is the following: point: Point on the surface of the unit sphere S² = {(x, y, z) € R³|x² + y² + z² = 1}. ● line: The great circles¹ of the unit sphere. ● lie on: A point p = (x, y, z) = S² lies on a great circle l if p = l.
4.
Recall that
Definition 1. Parallel Lines Two lines 1₁ and 12 are called parallel if
they don't intersect with each other.
(a) Discuss the 3-points model we explained in the lecture. Show that
there are no parallel lines in this model.
(b) Generalise the 3-points model to 4-points model, by giving the inter-
pretation to primitive terms and verifying axioms.
(c) Are there parallel lines in the 4-points model?
Transcribed Image Text:4. Recall that Definition 1. Parallel Lines Two lines 1₁ and 12 are called parallel if they don't intersect with each other. (a) Discuss the 3-points model we explained in the lecture. Show that there are no parallel lines in this model. (b) Generalise the 3-points model to 4-points model, by giving the inter- pretation to primitive terms and verifying axioms. (c) Are there parallel lines in the 4-points model?
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Bellman operator
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.
Similar questions
Recommended textbooks for you
Database System Concepts
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)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education