Seems I've stumbled upon one of the most confusing topics in discrete mathematics...My book does a terrible job of explaining how you actually create Hasse diagrams and only shows premade diagrams without explaining how they're constructed.
Example:
How on earth do you draw these things? The above diagram makes NO sense whatsoever to me. I already read this post about Hasse diagrams, but it didn't clear up my confusion as to how you actually go about drawing these things. In the above diagram for the partial order on the set of letters, how did they decide where each letter would go? Why are $B$ and $G$ off to the side? All of it seems very arbitrary to me and not at all intuitive.
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$\begingroup$A partially ordered set can be considered as a directed graph. In a Hasse diagram, the edges $u\rightarrow v$ are drawn in the plane such the node $u$ is drawn below the node $v$ and there is an undirected edge $u-v$. With this kind of drawing, you can drop the direction. Moreover, in a Hasse diagram, you don't draw transitive links. If $u\rightarrow v$ and $v\rightarrow w$, then $u\rightarrow w$ but you don't draw the link $u-w$. This gives you a very compact graphical representation of a poset.
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