I'm not really sure how to type this in notation...but I hope this makes sense. I help in proving that:
$$F \cap \bigcup\limits_{i=1}^\infty E_i = \bigcup\limits_{i=1}^\infty (F\cap E_i)$$
And
$$F \cup \bigcap\limits_{i=1}^\infty E_i = \bigcap\limits_{i=1}^\infty(F\cup E_i)$$
I really don't know where to begin with this one.