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

In summary, the conversation discusses the challenge of representing the relationship between the sets S, A, B, and C using a Venn diagram. It is noted that Set A and C are exclusive while Set B is inclusive in both A and C. The solution proposed is to relax the use of circles and allow for non-transverse configurations, by defining disjoint subsets B1 and B2 within B. This would result in a simple representation of the sets using an Euler diagram.
  • #1
haoku
24
0
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:
Physics news on Phys.org
  • #2
Don't use circles.
 
  • #3
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:
  • #4
Define B1 and B2 as disjoint subsets of B; B = B1 U B2.
 

1. What is a Venn diagram and how is it used to visualize relationships?

A Venn diagram is a graphical representation of relationships between different sets of data. It consists of overlapping circles or shapes that visually show the commonalities and differences between the sets. Venn diagrams can be used to compare and contrast different data sets, identify overlaps, and show relationships between different categories.

2. What are sets S, A, B, and C in a Venn diagram?

Sets S, A, B, and C are the different categories or groups that are being compared in the Venn diagram. Set S is the universal set, which includes all elements being considered. Set A and B are subsets of the universal set, and they represent specific categories or groups within the universal set. Set C represents the intersection of A and B, which includes elements that are common to both sets.

3. How do you determine the relationships between sets in a Venn diagram?

The relationships between sets in a Venn diagram can be determined by looking at the overlapping areas between the circles or shapes. If there is a common area between two sets, it indicates that there are elements that belong to both sets. If there is no overlap, it means that the two sets have no common elements. Additionally, the size of the circles or shapes can also indicate the size or quantity of elements in each set.

4. Can Venn diagrams be used to represent more than two sets?

Yes, Venn diagrams can be used to represent relationships between more than two sets. In these cases, more circles or shapes are added to the diagram to represent the additional sets. The overlapping areas can then show the relationships between multiple sets, such as common elements between three or four different categories.

5. How are Venn diagrams helpful in data analysis and problem-solving?

Venn diagrams are helpful in data analysis and problem-solving because they provide a visual representation of relationships between data sets. They can help identify patterns, similarities, and differences between different categories, and can also aid in making comparisons and finding commonalities. Venn diagrams can also be used to solve logic problems and make predictions based on the relationships between sets.

Similar threads

B Do any 3D Venn diagrams exist that have no 2D analogues?
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
949
I Implication, Boolean Expression and Venn Diagrams
    • Set Theory, Logic, Probability, Statistics
Replies
12
Views
5K
MHB Operations on Sets: Proving A⊆B⊆C & A∪B=B∩C
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
MHB Sets and Venn Diagrams for Real Numbers: Understanding Associative Axioms
    • Set Theory, Logic, Probability, Statistics
Replies
9
Views
4K
I When does ## { n \choose k } ## represent set of lists?
    • Set Theory, Logic, Probability, Statistics
Replies
20
Views
1K
B Cant get Venn diagram to agree with Demorgan's Law
    • Set Theory, Logic, Probability, Statistics
Replies
10
Views
2K
MHB Find 3-Set Venn Diagram: A,B,C w/ Empty Intersection
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
Disproving A=B with Counter Example: Sets A, B & C
    • Set Theory, Logic, Probability, Statistics
Replies
9
Views
3K
MHB Disjoint Sets R, T: Venn Diagram Visualization
    • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
Venn Diagram for set operations
    • Calculus and Beyond Homework Help
Replies
6
Views
1K

Hot Threads

Recent Insights

Back
Top