How to prove DeMorgan's Law?
$$A - (B \cup C) = (A - B) \cap (A - C)$$ $$A - (B \cap C) = (A - B) \cup (A - C)$$
EDIT:
Here is what I have tried so far:
Considering the first equation, assuming $x \in A - (B \cup C)$ then $x \in A$ and $x \not\in B$ and $x \not\in C$, while the right hand means ($x \in A$ and $x \not\in B$) or ($x \in A $ and $x \not\in C$) which is the same as $x \in A$ and $x \not\in B$ and $x \not\in C$. So the two set is the same.
But I do not know whether this is sufficient for a proof. Am I wrong?