## Solving a Venn Diagram Problem### Problem Statement:Use the given information to complete the solution of the partially solved Venn diagram.### Provided Data:- $ n(A) = 20 $ - $ n(B) = 20 $ - $ n(C) = 29 $- $ n(B \cap C) = 8 $ - $ n(S) = 51 $### Venn Diagram Explanation:The Venn diagram includes three circles labeled $ A $, $ B $, and $ C $, representing different sets within a universal set $ S $. Here is the breakdown of the sections within the Venn diagram that are filled or partially filled with numbers:1. **Intersection of A and B (excluding C)**: Contains number 4.2. **Intersection of all three sets (A, B, and C)**: Contains number 2.3. **Intersection of A and C (excluding B)**: Contains number 10.4. **Remaining sections**: These are left blank and need completion using the provided data.### Instructions:To complete the Venn diagram, calculate the missing values in each section that are currently blank, considering the intersecting and non-intersecting values provided and the cardinalities of each set. Utilize set operations and logical reasoning to determine the values for each blank section, ensuring the totals are accurate according to the problem statement.### Additional Information:This exercise combines principles of set theory and logical reasoning, often used in finite math and statistics to classify and organize data visually.

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Answered: Use the given information to complete…

Use the given information to complete the solution of the partially solved venn diagram. n(A) = 20, n(B) = 20, n(C) = 29, n(B N C) = 8, n(S) = 51 Figure Description S A В 4 10 Need Help? Read It

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

## Solving a Venn Diagram Problem

### Problem Statement:
Use the given information to complete the solution of the partially solved Venn diagram.

### Provided Data:
- $ n(A) = 20 $
- $ n(B) = 20 $
- $ n(C) = 29 $
- $ n(B \cap C) = 8 $
- $ n(S) = 51 $

### Venn Diagram Explanation:
The Venn diagram includes three circles labeled $ A $, $ B $, and $ C $, representing different sets within a universal set $ S $. Here is the breakdown of the sections within the Venn diagram that are filled or partially filled with numbers:

1. **Intersection of A and B (excluding C)**: Contains number 4.
2. **Intersection of all three sets (A, B, and C)**: Contains number 2.
3. **Intersection of A and C (excluding B)**: Contains number 10.
4. **Remaining sections**: These are left blank and need completion using the provided data.

### Instructions:
To complete the Venn diagram, calculate the missing values in each section that are currently blank, considering the intersecting and non-intersecting values provided and the cardinalities of each set. Utilize set operations and logical reasoning to determine the values for each blank section, ensuring the totals are accurate according to the problem statement.

### Additional Information:
This exercise combines principles of set theory and logical reasoning, often used in finite math and statistics to classify and organize data visually.

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