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

Prove

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

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- Feb 4th 2010, 04:54 PMtigergirlSubsets 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 $\displaystyle A\sim(B\cup C)=(A\sim B)\cup (A\sim C)$ and $\displaystyle A\sim(B\cup C)=(A\sim B)\cap(A\sim C)$ - Feb 5th 2010, 02:47 PMNyrox
First of all, does $\displaystyle A \sim B$ mean all elements in $\displaystyle A$ that are not in $\displaystyle B$? If so, then there are two things to point out: the first equality is wrong, it should read

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

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?