This might be a silly question, but somehow I cannot get my head around it. Suppose there are two sets of sets, $X_p$ for all $p \in P$, and $X_q$ for all $q \in Q$. If it holds that: $$ \forall p \in P, \exists q \in Q : X_p \subseteq X_q,$$
then $$\bigcup_{p \in P} X_p \subseteq \bigcup_{q \in Q} X_q.$$
But I cannot understand why this holds. Moreover, are these two representations equivalent?