n(A) = 15, n(B) = 10, n(C) = 31, n(S) = 39

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Title: Analyzing a Venn Diagram

**Introduction**

This section explores a Venn diagram used for understanding the relationships between different sets. The information provided gives insight into set memberships and their intersections.

**Set Definitions:**

- \( n(A) = 15 \) 
- \( n(B) = 10 \) 
- \( n(C) = 31 \) 
- Universal Set \( n(S) = 39 \)

**Description of the Venn Diagram:**

The diagram consists of three overlapping circles labeled \( A \), \( B \), and \( C \), enclosed within a rectangle representing the universal set \( S \). 

1. **Regions:**
   - **Intersection of A and B, excluding C**: Contains the value 0.
   - **Intersection of A and C, excluding B**: Contains the value 10.
   - **Intersection of B and C, excluding A**: Contains the value 5.
   - **Intersection of all three sets A, B, and C**: Contains the value 1.

2. **Unique Regions**:
   - Each circle also has unique, non-overlapping sections but they are not labeled with values in this diagram.

**Conclusion**

The Venn diagram helps visualize the distribution and intersection of elements across the sets \( A \), \( B \), \( C \), and their relationships within the universal set \( S \). This visual tool aids in comprehending complex set relationships and calculating intersections or exclusivities within given data sets.
Transcribed Image Text:Title: Analyzing a Venn Diagram **Introduction** This section explores a Venn diagram used for understanding the relationships between different sets. The information provided gives insight into set memberships and their intersections. **Set Definitions:** - \( n(A) = 15 \) - \( n(B) = 10 \) - \( n(C) = 31 \) - Universal Set \( n(S) = 39 \) **Description of the Venn Diagram:** The diagram consists of three overlapping circles labeled \( A \), \( B \), and \( C \), enclosed within a rectangle representing the universal set \( S \). 1. **Regions:** - **Intersection of A and B, excluding C**: Contains the value 0. - **Intersection of A and C, excluding B**: Contains the value 10. - **Intersection of B and C, excluding A**: Contains the value 5. - **Intersection of all three sets A, B, and C**: Contains the value 1. 2. **Unique Regions**: - Each circle also has unique, non-overlapping sections but they are not labeled with values in this diagram. **Conclusion** The Venn diagram helps visualize the distribution and intersection of elements across the sets \( A \), \( B \), \( C \), and their relationships within the universal set \( S \). This visual tool aids in comprehending complex set relationships and calculating intersections or exclusivities within given data sets.
The image contains a Venn diagram with three intersecting circles labeled A, B, and C within a universal set S. The following details are provided:

- \( n(A) = 19 \)
- \( n(B) = 20 \)
- \( n(C) = 29 \)
- \( n(B \cap C) = 8 \)
- \( n(S) = 50 \)

### Diagram Description:
- **Circle A** is in the upper left. Its intersection with **Circle B** contains the number 4.
- **Circle B** is in the upper right. In the overlapping area of all three circles, the number 2 is present.
- **Circle C** is at the bottom. The intersection of Circles A and C contains the number 10.
- There are rectangular placeholders in different regions of the Venn diagram, possibly indicating areas for additional data or labels.

This diagram is useful for understanding set relations and intersections in a universal set context.
Transcribed Image Text:The image contains a Venn diagram with three intersecting circles labeled A, B, and C within a universal set S. The following details are provided: - \( n(A) = 19 \) - \( n(B) = 20 \) - \( n(C) = 29 \) - \( n(B \cap C) = 8 \) - \( n(S) = 50 \) ### Diagram Description: - **Circle A** is in the upper left. Its intersection with **Circle B** contains the number 4. - **Circle B** is in the upper right. In the overlapping area of all three circles, the number 2 is present. - **Circle C** is at the bottom. The intersection of Circles A and C contains the number 10. - There are rectangular placeholders in different regions of the Venn diagram, possibly indicating areas for additional data or labels. This diagram is useful for understanding set relations and intersections in a universal set context.
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