If a set is a subset of an infinte intersection, then the compliment is a superset of the infinite union So as the title states I am trying to prove the following:
Show that if E ⊆ $\bigcap_{\alpha \in J}F_{\alpha}$, then $E^c \supseteq \bigcup_{\alpha \in J}F^c _{\alpha}$
I know that I should start by arguing: if $x \in \bigcup_{\alpha \in J}F^c _{\alpha}$ then $ x \notin F^{\alpha}$ for some $\alpha \in J$ However I have no idea where to go from here. 
Any help is much appreciated, thanks.

$E \subseteq \bigcap_i F_i$ implies the complements reverse, so
$$
\left(\bigcap_i F_i\right)^c \subseteq E^c
$$
and now apply DeMorgan's Law. 
