Partial Ordering/Examples/Ancestry

Example of Partial Ordering
Let $P$ denote the set of all people who have ever lived.

Let $\DD$ denote the relation on $P$ defined as:
 * $a \mathrel \DD b$ $a$ is a descendant of or the same person as $b$.

Its dual $\DD^{-1}$ is defined as:


 * $a \mathrel {\DD^{-1} } b$ $a$ is an ancestor of or the same person as $b$.

Then $\DD$ and $\DD^{-1}$ are partial orderings on $P$.