   Chapter 8.2, Problem 32ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# In 9-33, determine whether the given relation is reflexive, symmetric, transitive, or none of these. Justify your answer. Let A be the set of all lines in the plane. A relation R is defined on A as follows: For every l 1 and l 2 in A , l 1 R l 2 ⇔ l 1 is parallel to l 2 . (Assume that a line is parallel to itself.)

To determine

To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Explanation

Given information:

Let A be the set of all lines in the plane. A relation R is defined on A as follows:

For all l1 and l2 in A, l1R l2 ⇔ l1 is parallel to l2. (Assume that a line is parallel to itself.)

Calculation:

A − Set of all lines in a plane.

R is a relation on A defined by, l1,l2A, l1 R l2l1 is parallel to l2.

Reflexive:

By assumption, a line is parallel to itself, hence, lAl R l.

It is reflexive

Symmetric:

Let l1,l2A,

l1 R l2l1 is parallel to l2

l2 is parallel to  l1l2

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