Ordering/Examples/American Presidency

Example of Ordering
Let $S$ denote the set of.

Let $\PP$ denote the relation on $S$ defined as:
 * $a \mathrel \PP b$ $a$ was  after or at the same time as $b$.

Because was  both before and after, $\PP$ is not an antisymmetric relation.

Thus $\PP$ is not an ordering on $S$.