   Chapter 8.5, Problem 44ES ### 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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# Use the algorithm given in the text find a topological sorting for the relation of exercise 16(a) that is different from the “less than or equal to” relation ≤ .

To determine

To find:

A topological sorting for the “divides” relation on the set A={1,2,4,5,10,15,20}.

Explanation

Given information:

A={1,2,4,5,10,15,20}.

Concept used:

Hasse Diagram: It is a mathematical diagram representing a partially ordered set with finite number or members involving transitive reduction.

Calculation:

The set has one minimal element 1, so you can pick 1. The beginning of the total order is 1, with a total order of 1.

Set A1=A{3}. You can indicate this by removing 1 from the Hasse diagram as shown below.

Next, choose a minimal element from A1{1}. Thus, there are two minimal elements 2 and 5.

Either one may be chosen, pick 5. The total order thus far is total order 15.

Set A1=A{1}{5}=A{1,5}

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