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

Suggested languages for you:

Americas

Europe

Q21E

Expert-verified
Found in: Page 631

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# Draw the Hasse diagram for the less than or equal to relation on $$\{ 0,2,5,10,11,15\}$$.

The Hasse diagram for $$\{ (0,2,5,10,11,15), \le \}$$

See the step by step solution

## Step 1: Given data

Given data is $$(0,2,5,10,11,15)$$.

## 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 greater than or equal to relation on $$\{ 0,2,5,10,11,15\}$$ which is represented as $$\{ (0,2,5,10,11,15), \le \}$$. The Hasse diagram for $$\{ (0,2,5,10,11,15), \le \}$$

Hence, Hasse diagram for less than or equal to relation on $$\{ 0,2,5,10,11,15\}$$ is drawn.