Drawing Hasse Diagrams for Divisibility Relations

  • Thread starter Thread starter mblack
  • Start date Start date
  • Tags Tags
    Diagrams Drawing
Click For Summary
SUMMARY

The discussion focuses on constructing a Hasse diagram for the divisibility relation defined on the set X={1,2,3,5,6,10,15,30}. Participants emphasize starting with the smallest element that divides others without intermediate elements, ensuring edges only connect directly related elements. The key takeaway is the importance of identifying minimal elements and direct relationships in the diagram. A reference to a Wikipedia article on Hasse diagrams is provided as a resource for further understanding.

PREREQUISITES
  • Understanding of divisibility relations in set theory
  • Familiarity with Hasse diagrams and their properties
  • Basic graph theory concepts
  • Ability to interpret mathematical notation and relations
NEXT STEPS
  • Study the construction of Hasse diagrams in detail
  • Explore examples of divisibility relations in set theory
  • Learn about the properties of partially ordered sets (posets)
  • Review graph theory fundamentals to enhance diagram drawing skills
USEFUL FOR

Students studying discrete mathematics, educators teaching set theory concepts, and anyone interested in visualizing mathematical relationships through Hasse diagrams.

mblack
Messages
10
Reaction score
0

Homework Statement


Draw the diagram P=(X,P) where X={1,2,3,5,6,10,15,30} and x<y in P IFF x divides y.


Homework Equations





The Attempt at a Solution


We just started this discussion in class and I am really not getting the concept of how to draw the corresponding Hasse diagram. I know that I am supposed to start with the smallest x for which x<y and for which there does not exist a z such that x<z<y. However, I don't know whether that should be a single element or an ordered pair when I list it on the diagram. I also know that I am only supposed to draw an edge if x is the preceding element to y. Anyway, that is pretty much all I understand about this concept. I appreciate any help in explanation of this concept.
 
Physics news on Phys.org
mblack said:

Homework Statement


Draw the diagram P=(X,P) where X={1,2,3,5,6,10,15,30} and x<y in P IFF x divides y.


Homework Equations





The Attempt at a Solution


We just started this discussion in class and I am really not getting the concept of how to draw the corresponding Hasse diagram. I know that I am supposed to start with the smallest x for which x<y and for which there does not exist a z such that x<z<y. However, I don't know whether that should be a single element or an ordered pair when I list it on the diagram. I also know that I am only supposed to draw an edge if x is the preceding element to y. Anyway, that is pretty much all I understand about this concept. I appreciate any help in explanation of this concept.

There's an article in wikipedia--http://en.wikipedia.org/wiki/Hasse_diagram. Maybe that will serve as a starting point for you.
 
Last edited by a moderator:

Similar threads

How to draw phase portrait for 2x2 nonlinear system of DE?
  • · Replies 1 ·
Replies
1
Views
2K
Plotting a Scatter Diagram from a Large Data Set
  • · Replies 4 ·
Replies
4
Views
2K
Drawing sets of Complex Variables
  • · Replies 14 ·
Replies
14
Views
2K
Hasse diagram: minimal, least, greatest
  • · Replies 1 ·
Replies
1
Views
2K
Relationship between autonomous system and related single equation
  • · Replies 3 ·
Replies
3
Views
2K
How to Interpret the Basic Logic Problem with Predicate P(x,y,z)
  • · Replies 2 ·
Replies
2
Views
2K
Writing some ZF axioms with FOL symbols
  • · Replies 2 ·
Replies
2
Views
2K
Drawing physics Diagrams with online software
  • · Replies 7 ·
Replies
7
Views
8K
Undergrad Teaching Minkowski diagrams effectively
  • · Replies 15 ·
Replies
15
Views
3K
A line integral about a closed "unit triangle" around the origin
  • · Replies 12 ·
Replies
12
Views
5K