Find the set Anø. U= {1, 2, 3, 4, 5, 6, 7} A = {4, 5, 6, 7} Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. Ano- (Use a comma to separate answers as needed.) OB. Anø is the empty set.
Find the set Anø. U= {1, 2, 3, 4, 5, 6, 7} A = {4, 5, 6, 7} Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. Ano- (Use a comma to separate answers as needed.) OB. Anø is the empty set.
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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Question
26
![**Educational Content: Intersection of Sets and the Empty Set**
---
**Problem Statement:**
Find the set \(A \cap \emptyset\).
Given:
\[ U = \{1, 2, 3, 4, 5, 6, 7\} \]
\[ A = \{4, 5, 6, 7\} \]
**Instructions:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \(A \cap \emptyset = \{\} \) (Use a comma to separate answers as needed.)
- B. \(A \cap \emptyset\) is the empty set.
---
**Explanation:**
The intersection of any set \(A\) with the empty set \(\emptyset\) is always the empty set. This is because there are no elements common to any set \(A\) and \(\emptyset\). Therefore:
\[A \cap \emptyset = \emptyset\]
So, the correct answer is:
**B.** \(A \cap \emptyset\) is the empty set.
---
This content demonstrates fundamental concepts in set theory, specifically focusing on the intersection of sets and the properties of the empty set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2da42e1f-052a-4cf5-8e01-3c98d930576f%2F1fbebb79-6f73-4bf5-abf5-931517b58f41%2Fgtbqj4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Intersection of Sets and the Empty Set**
---
**Problem Statement:**
Find the set \(A \cap \emptyset\).
Given:
\[ U = \{1, 2, 3, 4, 5, 6, 7\} \]
\[ A = \{4, 5, 6, 7\} \]
**Instructions:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \(A \cap \emptyset = \{\} \) (Use a comma to separate answers as needed.)
- B. \(A \cap \emptyset\) is the empty set.
---
**Explanation:**
The intersection of any set \(A\) with the empty set \(\emptyset\) is always the empty set. This is because there are no elements common to any set \(A\) and \(\emptyset\). Therefore:
\[A \cap \emptyset = \emptyset\]
So, the correct answer is:
**B.** \(A \cap \emptyset\) is the empty set.
---
This content demonstrates fundamental concepts in set theory, specifically focusing on the intersection of sets and the properties of the empty set.
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