prove a statement (complements of unions) I want to prove this statement:
$$(A_1 \cup A_2)^c  =  {A_1}^c \cup {A_2}^c$$
where the $c$ means the complement.
Any help would be greatly appreciated.

This is false in the general case. For example, if $A_1$ is the set of integers ($\{\ldots,-2,-1,0,1,2,\ldots\}$) and $A_2$ is the set of positive real numbers, and the universe is the set of all real numbers, then  $(A_1 \cup A_2)^c$ doesn't contain $-1$ or $\frac12$, but $A_1^c \cup A_2^c$ contains them.
