Discrete math venn diagram proof

AI Thread Summary
To prove that A complement UNION B complement equals (A intersect B) complement, drawing Venn diagrams can effectively illustrate the relationship between the sets. By shading the areas for both sides of the equation, one can visually confirm they represent the same region, regardless of whether sets A and B are disjoint or overlapping. While some may not consider this method a rigorous proof, it serves as a useful visual aid. Understanding how to indicate components like union and complement in Venn diagrams is crucial for this proof. For further clarification, exploring DeMorgan's laws can provide additional insights into the topic.
leilei
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Prove for all sets A,B, and C :
A complement UNION B complement = (A intercept B) complement

help me out here please
 
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If you (or your teacher) finds drawing Venn diagrams sufficient as a proof, you can just draw two Venn diagrams for the cases where A and B are disjoint or have an overlap and show that if you shade the left hand side or the right hand side, you will get the same shaded area. (I personally wouldn't consider that a real hard proof, however).
Do you know how to indicate the different components in a Venn diagram (e.g. union, complement, etc)?
 
this proof is to show why the two pictures/diagram are the same...
 
So, do you know how to draw Venn diagrams at all? Because if not, then the problem is not in the proof but in drawing the diagrams. And if you do, there is nothing to it, but drawing them.

Also, you asked this question before, right?
 
You can also try googling DeMorgan's laws for more information.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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