   Chapter 8.1, Problem 17ES ### 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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# Draw the directed graphs of the relations defined in 13-18.Let A = { 2 , 3 , 4 , 5 , 6 , 7 , 8 } and define a relation T on A as follows: For every x , y ∈ A , x T y                             ⇔ 3 | ( x − y ) .

To determine

Draw the directed graph of the relation.

Explanation

Given information:

For all x,yA, and A={2,3,4,5,6,7,8}.

For all x,yA, x T y3|(xy).

Calculation:

The arrows between two numbers (or the number and itself) must differ by a multiple of 3

(i.e., 0, 3 or 6) in order for 3|(xy).

2 T 23 T 3T 4T 56T6T 7T8T 58 T 2T 4T 35 T 22 T 5T 6T 7T 82T 8

Thus, the relation T is then:

T={(5,5

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