Answer these two questions if you can, these questions deals with set operations and Venn diagram. Answer correctly. **Problem Statement:**3. Which set represents the intersection of sets \(A\), \(B\), and \(C\) shown in the diagram below?**Venn Diagram Description:**- The diagram displays three intersecting circles labeled \(A\), \(B\), and \(C\).- Elements are distributed across different regions created by the overlapping circles. - **Region in circle \(A\) only:** 1 - **Region in circle \(B\) only:** 8 - **Region in circle \(C\) only:** 9 - **Intersection of \(A\) and \(B\) only:** 3 - **Intersection of \(A\) and \(C\) only:** 4, 7 - **Intersection of \(B\) and \(C\) only:** 6 - **Intersection of all three circles \(A\), \(B\), and \(C\):** 2 - **Intersection of \(A\) and \(B\) and \(C\):** 5**Options:**A. \(\{3, 4, 5, 6, 7\}\)B. \(\{2\}\)C. \(\{2, 3, 4, 5, 6, 7\}\)D. \(\{1, 2, 3, 4, 5, 6, 7, 8, 9\}\)**Correct Answer:**The intersection of sets \(A\), \(B\), and \(C\) includes only the elements common to all three sets, which are found in the area where all three circles overlap.- **Answer: B. \(\{2\}\)** ### Problem 5Given the sets:- \( A = \{0, 1, 3, 4, 6, 7\} \)- \( B = \{0, 2, 3, 5, 6\} \)- \( C = \{0, 1, 4, 6, 7\} \)Determine the intersection of the three sets, \( A \cap B \cap C \).### Options:A. \(\{0, 1, 2, 3, 4, 5, 6, 7\}\)B. \(\{0, 3, 6\}\)C. \(\{0, 6\}\)D. \(\{0\}\)### Explanation:To solve this problem, we need to find the common elements that belong to all three sets \( A \), \( B \), and \( C \). Calculate the intersection step-by-step to arrive at the correct answer.

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Answered: 3. Which set represents the…

Math

Probability

3. Which set represents the intersection of sets A, B, and C shown in the diagram below?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Answer these two questions if you can, these questions deals with set operations and Venn diagram. Answer correctly.

**Problem Statement:**

3. Which set represents the intersection of sets \(A\), \(B\), and \(C\) shown in the diagram below?

**Venn Diagram Description:**

- The diagram displays three intersecting circles labeled \(A\), \(B\), and \(C\).
- Elements are distributed across different regions created by the overlapping circles.

- **Region in circle \(A\) only:** 1
- **Region in circle \(B\) only:** 8
- **Region in circle \(C\) only:** 9
- **Intersection of \(A\) and \(B\) only:** 3
- **Intersection of \(A\) and \(C\) only:** 4, 7
- **Intersection of \(B\) and \(C\) only:** 6
- **Intersection of all three circles \(A\), \(B\), and \(C\):** 2
- **Intersection of \(A\) and \(B\) and \(C\):** 5

**Options:**

A. \(\{3, 4, 5, 6, 7\}\)

B. \(\{2\}\)

C. \(\{2, 3, 4, 5, 6, 7\}\)

D. \(\{1, 2, 3, 4, 5, 6, 7, 8, 9\}\)

**Correct Answer:**

The intersection of sets \(A\), \(B\), and \(C\) includes only the elements common to all three sets, which are found in the area where all three circles overlap.

- **Answer: B. \(\{2\}\)**

### Problem 5

Given the sets:

- \( A = \{0, 1, 3, 4, 6, 7\} \)
- \( B = \{0, 2, 3, 5, 6\} \)
- \( C = \{0, 1, 4, 6, 7\} \)

Determine the intersection of the three sets, \( A \cap B \cap C \).

### Options:

A. \(\{0, 1, 2, 3, 4, 5, 6, 7\}\)

B. \(\{0, 3, 6\}\)

C. \(\{0, 6\}\)

D. \(\{0\}\)

### Explanation:

To solve this problem, we need to find the common elements that belong to all three sets \( A \), \( B \), and \( C \). Calculate the intersection step-by-step to arrive at the correct answer.

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