• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q22E

Expert-verified Found in: Page 631 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # 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 See the step by step solution

## 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. ### Want to see more solutions like these? 