   Chapter 8.2, Problem 33ES ### 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 defines on A as follows. For every l 1 and l 2 in A. l 1   R   l 2   ⇔ l 1   is   perpendicular to  l 2 .

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 perpendicular to l2.

Calculation:

A= Set of all lines in the plane

R={(p,q)A×A|p is perpendicular to q}

Reflexive:

The relation R is reflective if (p,p)R for every element pA.

Since a line is never perpendicular to itself, (p,p)R.

Thus, R is not reflexive.

Symmetric:

The relation R on a set A is symmetric if (q,p)R whenever (p,q)R

Let us assume that (p,q)R

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