# Math Help - Subsets using DeMorgan's Law(23)

1. ## Subsets using DeMorgan's Law(23)

I having problems with these two questions. I know that both deals the DeMorgan's law but dont know what to do.

Prove

If $A\sim(B\cup C)=(A\sim B)\cup (A\sim C)$ and $A\sim(B\cup C)=(A\sim B)\cap(A\sim C)$

2. First of all, does $A \sim B$ mean all elements in $A$ that are not in $B$? If so, then there are two things to point out: the first equality is wrong, it should read

$A\sim (B \cap C)=(A\sim B)\cup (A\sim C)$ ( $\cap$ on the leftt side, not $\cup$ )

and both of them are the actual statement of De Morgan's laws for sets. So, is your question: how do you prove De Morgan's laws?