Answered: b) On the set L of all straight lines…

b) On the set L of all straight lines into the plane, we define a relation R as follows: 1, R1, if and only if 1 is parallel to 1, or 1=12 1. determines whether R is an equivalence relation.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 28E

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Question

part b

a) In a square with a side length of 8 cm, 17 points are randomly placed. Show that there
are guaranteed to be two points with a mutual distance of no more than 2.9cm.
b) On the set L of all straight lines into the plane, we define a relation R as follows:
1, R1, if and only if 1 is parallel to 1, or 11 =12
1. determines whether R is an equivalence relation.
2. determines whether R is a partial order relationship.
3.

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