   Chapter 8.1, Problem 16ES ### 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 = { 5 , 6 , 7 , 8 , 9 , 10 } and define a relation S on A as follows: For every x , y ∈ A . x S y         ⇔ 2 | ( x − y ) .

To determine

Draw the directed graph of the relation.

Explanation

Given information:

A={5,6,7,8,9,10} and relation S is defined as

For all x,yA, x S y2|(xy).

Calculation:

x S y holds when 2|(xy) and thus when x − y is divisible by 2. However, x − y is divisible by 2 when x and y are both even, but also when x and y are both odd.

5 S 55 S 7S 9S 5S 7S 9S 5S 79 S 9S 6S 8S 108 S 68 S 88 S 1010 S 610 S 810 S 10

Thus, the relation S is then:

S={(5,5)

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