StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q21E

Expert-verifiedFound in: Page 631

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 \(\{ (0,2,5,10,11,15), \le \} \)

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

**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).**

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.

94% of StudySmarter users get better grades.

Sign up for free