Given a simple oriented graph $G$, let $\theta(G)$ be the clique covering number of G (i.e. the minimum number of cliques needed to cover the vertices of G) and $m(G)$ be the number of maximal cliques of $G$. For example, for the 5-cycle $C_5$, $\theta(C_5) = 3$ and $m(C_5) = 5$ (since there are 5 2-cliques).
Given a graph G, why does $\theta(G) \leq m(G)$ ? (equality for every induced graph is the definition of trivially perfect graphs).
Should be trivial, but I'm missing something.
Every vertex belongs to a maximal clique. By taking the set of all maximal cliques you cover all the vertices (e.g. all $2$-cliques from your example), so $m(G)\geq\theta(G)$.