   Chapter 8.5, Problem 45ES ### 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 to find a to-pological sorting for the relation of exercise 16(b) 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={2,3,4,6,8,12,18}.

Explanation

Given information:

A={2,3,4,6,8,12,18}.

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 two minimal elements 2 and 3. Either one may be chosen, say pick 3.

The beginning of the total order is

Total order: 3

Set A1=A{3}, you can indicate this by removing 3 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}. You can indicate this by removing 5 from the Hasse diagram as follows.

Next, choose the minimal element from A1{3}

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