Visualizing Relationships with Venn Diagrams and Sets S, A, B, C

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Discussion Overview

The discussion revolves around visualizing relationships between sets S, A, B, and C using Venn diagrams. The focus is on how to represent these sets, particularly addressing the challenges posed by their inclusivity and exclusivity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that sets A (even numbers) and C (odd numbers) are exclusive and do not overlap, while set B (positive integers) is inclusive of both A and C, raising questions about how to represent this in a Venn diagram.
  • Another participant proposes not to use circles at all for the representation.
  • A different viewpoint suggests relaxing the requirement for circles to simple closed curves and allowing non-transverse configurations, indicating that this could simplify the representation while still being an Euler diagram.
  • A participant introduces the idea of defining subsets B1 and B2 as disjoint subsets of B, suggesting a union of these subsets to address the representation issue.

Areas of Agreement / Disagreement

Participants express differing opinions on the appropriate method for visualizing the relationships among the sets, indicating that multiple competing views remain without a consensus on the best approach.

Contextual Notes

The discussion highlights limitations in the traditional Venn diagram approach when dealing with sets that have both inclusivity and exclusivity, as well as the potential complexity introduced by the subsets of B.

haoku
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Given S is set for all real number. A is set for all even number, B is set for all positive integer, C is set for odd number represent the relationship between the sets with Venn diagram.
This question is seems easy. However, there is a problem that how can we illustrate the three sets in circles. Set A and C are exclusive so they do not touch each other. However, For Set B, it is totally inclusive in Set A and C. How should we draw the Circle for Set B?
 
Last edited:
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Don't use circles.
 
haoku said:
Given S is set for all real number. A is set for all even number, B is set for all positive integer, C is set for odd number represent the relationship between the sets with Venn diagram.
This question is seems easy. However, there is a problem that how can we illustrate the three sets in circles. Set A and C are exclusive so they do not touch each other. However, For Set B, it is totally inclusive in Set A and C. How should we draw the Circle for Set B?

Relax circle to simple closed curve.
Admit non-transverse configurations (curves touching without crossing).
Then your problem has a simple representation, and it's still an Euler diagram.
 
Last edited:
Define B1 and B2 as disjoint subsets of B; B = B1 U B2.
 

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