 Example 1.  Let \(E = \{a, b, c, d, e\}\) and \(P\) be the set of ordered pairs \(\{(a, c), (a, d), (a, e), (b, e), (c, e)\}\). Given A7, the relation \(O\) consists of the set of pairs \(\{(a, b), (b, c), (b, d), (c, d), (d, e)\}\).  \(E\) contains three maximal subsets of pairwise overlapping events, that is, instants \(i_1 = \{a, b\}\), \(i_2 = \{b, c, d\}\) and \(i_3 = \{d, e\}\). Furthermore, \(i_1\), \(i_2\) and \(i_3\) are linearly ordered as \(i_1 \lt i_2 \lt i_3\) because \(a \in i_1\), \(c \in i_2\) and \(P(a, c)\) hence \(i_1 \lt i_2\), and \(c \in i_2\), \(e \in i_3\) and \(P(c, e)\) hence \(i_2 \lt i_3\), and similarly for \(i_1 \lt i_3.\)  