Hasse Diagram for partial ordering 'x divides y' on set

[Pockt]

Hello,

I am working on a problem where I have to draw a Hasse Diagram for the partial ordering "x divides y" on the set {2, 3, 7, 21, 42, 105, 210}. Then I am asked to name any least elements, minimal elements, greastest elements, and maximal elements and to also name a totally ordered subset with four elements. I'm having trouble understanding the logic on how the numbers should placed within this diagram.

Any help is greatly appreciated!

 

[daon]

Re: Hasse Diagram!!

Each node must be a parent of all that are "less than" it in your set. Using division as the order on your set, 3 and 7 would be all the leaves of 21 (note not all elements are comparable, and your tree may not be connected). As for naming special elements... just look at the definitions you're working with after you've constructed your tree(s).