Discrete math venn diagram proof

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Discussion Overview

The discussion revolves around proving the set identity A complement UNION B complement = (A intersect B) complement using Venn diagrams. It includes aspects of proof techniques and visual representation in discrete mathematics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested, Homework-related

Main Points Raised

  • One participant requests help in proving the set identity using Venn diagrams.
  • Another participant suggests that drawing Venn diagrams for different cases (disjoint sets or overlapping sets) can visually demonstrate the equivalence of both sides of the equation, though they express skepticism about the rigor of this method as a proof.
  • A further reply emphasizes the importance of correctly drawing Venn diagrams to understand the proof, implying that the challenge may lie in the diagramming rather than the proof itself.
  • Another participant mentions that the original poster may have asked this question previously, hinting at a recurring difficulty.
  • One participant recommends looking up DeMorgan's laws for additional context and understanding related to the proof.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the adequacy of Venn diagrams as a proof method, with some expressing doubt about its rigor while others focus on the practical aspect of drawing the diagrams correctly.

Contextual Notes

There are limitations regarding the assumptions about the participants' familiarity with Venn diagrams and the definitions of set operations, which may affect their ability to engage with the proof effectively.

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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