Exercise 8.6.4

To prove property (o1), assume $A⊈B$. By definition, this means there is some $a\in A$ with $a\notin B$. From Exercise 8.6.2 this means $\forall <!--\; FUNCTION\; APPLICATION\; -->b\in B$, $b<a$. Then by property (c2) $b\in A$; hence $B\subseteq A$.

(o2) is a direct result of the definition of set equality, and (o3) is true because of transivity of the set inclusion relationship.