Drawing Hasse Diagrams for Divisibility Relations

[mblack]

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.

 

[Mark44]

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.