   Chapter 8.2, Problem 31ES ### 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 answers.31. Let A be the set of people living in the world today. A relation R is defined on A as follows: For all people p and q in A, p   R   q ⇔ p lives within 100 miles of q.

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 people living in the world today. A relation R is defined on A as follows:

For all p, q ∈ A, p R q ⇔ p lives within 100 miles of q.

Calculation:

A= set of people living in the world today

R={(p,q)A×A|p lives within 100 miles from q}

Reflexive:

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

Since a person always lives within 100 miles from itself, we know that (p,p)R for all elements pA. thus R is 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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