Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

To draw the Hasse diagram for divisibility on the set \(\{ 1,3,9,27,81,243\} \).

The Hasse diagram for divisibility on the set \(\{ 1,3,9,27,81,243\} \) is drawn as

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

For divisibility on the set \(\{ 2,3,5,10,11,15,25\} \)

Step 2: Concept used Hasse diagram

Hasse diagrams are obtained from a directed graph of a partial ordering by,

1) Removing all loops due to reflexivity from the graph of a partial ordering.

2) Removing all edges occurring due to transitivity of the partial ordering.

3) Arranging all edges to point upwards and deleting (directional) arrows

Thus to get all ordered pairs ordered pairs in the partial ordering for a given Hasse diagram, we look for pairs \((x,y)\) such that path from \(x\) to \(y\) is going upwards . In addition, we also need to add pairs of the form \((x,x)\) to account for reflexive pairs (loops).

Step 3: Draw the Hasse diagram

Consider for divisibility on the set \(\{ 1,3,9,27,81,243\} \).

The Hasse diagram for for divisibility on the set \(\{ 1,3,9,27,81,243\} \)

From the above Hasse diagram it is clear that, the every number divides next number in the set. Hence, The Hasse diagram for divisibility on the set \(\{ 1,3,9,27,81,243\} \) is drawn.

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Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

To draw the Hasse diagram for divisibility on the set \(\{ 1,3,9,27,81,243\} \).

Step by Step Solution

Step 1: Given data

Step 2: Concept used Hasse diagram

Step 3: Draw the Hasse diagram

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Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

To draw the Hasse diagram for divisibility on the set \(\{ 1,3,9,27,81,243\} \).

Step by Step Solution

Step 1: Given data

Step 2: Concept used Hasse diagram

Step 3: Draw the Hasse diagram

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