Drawing Hasse Diagrams for Divisibility Relations

In summary, the conversation discusses drawing a Hasse diagram for the set P = (X,P) where X = {1,2,3,5,6,10,15,30} and x < y in P IFF x divides y. The speaker is struggling with understanding the concept and is unsure how to represent it on the diagram. They mention starting with the smallest x for which x < y and drawing an edge only if x is the preceding element to y. They also mention finding more information on Hasse diagrams through Wikipedia.
  • #1
mblack
11
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.
 
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  • #2
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.
 
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Related to Drawing Hasse Diagrams for Divisibility Relations

1. What is a Hasse diagram?

A Hasse diagram is a visual representation of the partial order of a set, where the elements are represented as nodes and the relationships between them are represented as edges. It is a useful tool for understanding the structure of a partially ordered set.

2. How do you draw a Hasse diagram?

To draw a Hasse diagram, start by listing all the elements of the set in a vertical column. Then, draw a line connecting any two elements where the first element is less than or equal to the second element. Continue this process until all possible connections have been made. Finally, remove any redundant lines and rearrange the elements to create a more organized diagram.

3. What are the benefits of using Hasse diagrams?

Hasse diagrams provide a clear and concise visual representation of the relationships between elements in a partially ordered set. They also make it easier to identify the maximal and minimal elements, as well as the upper and lower bounds of the set.

4. Are there any limitations to using Hasse diagrams?

Hasse diagrams can become complex and difficult to read for larger sets with many elements and relationships. Additionally, they only represent partial orders and cannot be used for total orders or non-partial orders.

5. Can Hasse diagrams be used for any type of set?

Hasse diagrams are typically used for finite partially ordered sets, but they can also be used for infinite sets in some cases. However, they are not suitable for all types of sets, such as non-partially ordered sets or sets with a large number of elements.

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