Discrete math venn diagram proof

In summary, to prove that A complement UNION B complement is equal to the complement of A intersect B, you can draw two Venn diagrams for the cases where A and B are disjoint or have an overlap. By shading the left hand side or the right hand side, you can show that they have the same shaded area. This is known as DeMorgan's laws.
  • #1
leilei
8
0
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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  • #2
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)?
 
  • #3
this proof is to show why the two pictures/diagram are the same...
 
  • #4
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?
 
  • #5
You can also try googling DeMorgan's laws for more information.
 

1. What is a discrete math Venn diagram proof?

A discrete math Venn diagram proof is a method of proving the validity of a statement or theorem using Venn diagrams. It involves representing the elements and relationships between sets using overlapping circles, and using logical operations such as intersection, union, and complement to demonstrate the truth of the statement.

2. How do you create a Venn diagram for a discrete math proof?

To create a Venn diagram for a discrete math proof, start by identifying the sets involved in the statement. Draw circles for each set, with the overlapping region representing the intersection of the sets. Use shading or labeling to show the elements in each set, and use logical operations to show the relationships between the sets.

3. What are the advantages of using a Venn diagram in a discrete math proof?

Venn diagrams are a visual and intuitive way to represent and analyze sets and their relationships. They allow for a clearer understanding of the logic and structure of a proof, and can make it easier to identify errors or gaps in reasoning.

4. What are some common mistakes to avoid when using a Venn diagram in a discrete math proof?

Some common mistakes to avoid when using a Venn diagram in a discrete math proof include not labeling the sets accurately, not properly representing the relationships between sets, and making incorrect assumptions or conclusions based on the diagram.

5. Can a Venn diagram be used to prove any statement in discrete math?

No, a Venn diagram is not a universal proof method and cannot be used to prove all statements in discrete math. Some statements may require other methods of proof, such as mathematical induction or direct proof. Venn diagrams are most useful for proving set identities, set membership, and other statements involving sets and their relationships.

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