Elementary Foundations: An introduction to topics in discrete mathematics

Let $A=\{2,4,6,8,10,12\}\text{.}$ The Hasse diagram of the partial order $\mid$ (i.e. “divides”) on $A$ appears in Figure 19.3.2. Notice that $2$ is not joined directly to either $8$ or $12\text{,}$ since we can use transitivity and the facts that $2\mid 4$ and $2\mid 6$ to infer $2\mid 8$ and $2\mid 12\text{,}$ respectively, from the diagram.

The graph from Example 14.4.1 has been reproduced in Figure 19.3.5 as a Hasse diagram, and represents the partial order $\subseteq$ on $\mathcal{P}(\{a,b,c\})\text{.}$