Discrete math venn diagram proof

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SUMMARY

The discussion centers on proving the set theory identity A complement UNION B complement = (A intersect B) complement using Venn diagrams. Participants suggest that drawing Venn diagrams for both disjoint and overlapping sets A and B can visually demonstrate the equivalence of the two sides of the equation. While some participants consider this method insufficient as a rigorous proof, it effectively illustrates the relationship between the sets. Additionally, references to DeMorgan's laws provide further context for understanding the proof.

PREREQUISITES
  • Understanding of set theory concepts, specifically complements and intersections.
  • Familiarity with Venn diagram notation and representation.
  • Knowledge of DeMorgan's laws in set theory.
  • Basic skills in visual representation of mathematical concepts.
NEXT STEPS
  • Research DeMorgan's laws and their applications in set theory.
  • Practice drawing Venn diagrams for various set operations.
  • Explore formal proofs in set theory to understand rigorous proof techniques.
  • Study the properties of unions and intersections in set theory.
USEFUL FOR

Students of discrete mathematics, educators teaching set theory, and anyone seeking to understand the visual representation of set operations through Venn diagrams.

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.
 

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