De Morgan's Rules
− (A ∪ B) = − A ∪ − B, − (A ∩ B) = − A ∪ − B
Let me demonstrate why I'm confused about the first equality:
U = {1,2,3,4} A = {2} B = {3}
− (A ∪ B) = {1,4}
-A = {1,3,4} -B = {1,2,4}
− A ∪ − B = {1,2,3,4}

So you can see I don't see how the result is equal sets.

Question

De Morgan's Rules
− (A ∪ B) = − A ∪ − B, − (A ∩ B) = − A ∪ − B
Let me demonstrate why I'm confused about the first equality:
U = {1,2,3,4} A = {2} B = {3}
− (A ∪ B)  = {1,4}
-A = {1,3,4} -B = {1,2,4}
− A ∪ − B = {1,2,3,4}

So you can see I don't see how the result is equal sets.

anonymous · Answer

that is not what demorgan says

anonymous · Answer

That's because you've misstated DeMorgan's rules. The complement of the union is the INTERSECTION of the complements, not the union of the complements.

anonymous · Answer

$$\lnot (A\cap B)=\lnot A \cup \lnot B$$

anonymous · Answer

and 
$$\lnot (A\cup B)=\lnot A\cap \lnot B$$

anonymous · Answer

My book is playing tricks with me.... I copy pasted.

anonymous · Answer

when you remove the parentheses, change intersection to union and union to intersection

anonymous · Answer

Yeah I'm worried though about pursuing the rest o fthe book if they made this mistake.Thanks for the clarification.