I have a proof that if $A$ and $B$ are in the Event Space ($F$) then $A-B\in F$. However, I don't think it's very elegant. Do people have another proof that is perhaps more elegant?
Here is the proof: $A,B \in F $
$\implies A \cup B \in F$ ... ($X_1,X_2,\in F \implies X_1\cup X_2\in F$)
$\implies (S-A)\cup B \in F$ ... ($X\in F\implies S-A \in F$)
$\implies S - [(S-A)\cup B] \in F$ ... ($X\in F\implies S-A \in F$)
$\implies A\cap (S-B) \in F$ ... (by DeMorgan's Law)
$\implies A-B \in F$
Thank you!