Which of the following sets are equal? (Select all that apply.) OA = {4, 5, 6} B = {xER| 3
Which of the following sets are equal? (Select all that apply.) OA = {4, 5, 6} B = {xER| 3
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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Transcribed Image Text:**Question:**
Which of the following sets are equal? (Select all that apply.)
1. \( A = \{4, 5, 6\} \)
2. \( B = \{ x \in \mathbb{R} \mid 3 \leq x < 7 \} \)
3. \( C = \{ x \in \mathbb{R} \mid 3 < x < 7 \} \)
4. \( D = \{ x \in \mathbb{Z} \mid 3 < x < 7 \} \)
5. \( E = \{ x \in \mathbb{Z}^+ \mid 3 < x < 7 \} \)
**Explanation:**
- \( A \) is the set containing the integers 4, 5, and 6.
- \( B \) is the set of real numbers \( x \) such that \( x \) is greater than or equal to 3 and less than 7.
- \( C \) is the set of real numbers \( x \) such that \( x \) is greater than 3 and less than 7.
- \( D \) is the set of integers \( x \) such that \( x \) is greater than 3 and less than 7, which includes 4, 5, and 6.
- \( E \) is the set of positive integers \( x \) such that \( x \) is greater than 3 and less than 7, which also includes 4, 5, and 6.
**Graphs/Diagrams:**
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Transcribed Image Text:### Subset and Proper Subset Analysis
This document contains multiple set comparison exercises to determine if one set is a subset or a proper subset of another. Each section contains a question, options for answers, and the correct choice indicated with a filled option.
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**(d)**
- **Sets Defined:**
- \( A = \{a, b, c\} \)
- \( B = \{\{a\}, \{b\}, \{c\}\} \)
- **Questions:**
1. Is \( A \subseteq B \)?
- Options:
- Yes
- **No** (Correct)
2. Is \( B \subseteq A \)?
- Options:
- Yes
- **No** (Correct)
3. Is either \( A \) or \( B \) a proper subset of the other?
- Options:
- Yes, \( A \) is a proper subset of \( B \).
- Yes, \( B \) is a proper subset of \( A \).
- **No, neither is a proper subset of the other.** (Correct)
---
**(e)**
- **Sets Defined:**
- \( A = \{\sqrt{36}, \{6\}\} \)
- \( B = \{6\} \)
- **Questions:**
1. Is \( A \subseteq B \)?
- Options:
- Yes
- **No** (Correct)
2. Is \( B \subseteq A \)?
- Options:
- **Yes** (Correct)
- No
3. Is either \( A \) or \( B \) a proper subset of the other?
- Options:
- Yes, \( A \) is a proper subset of \( B \).
- **Yes, \( B \) is a proper subset of \( A \).** (Correct)
- No, neither is a proper subset of the other.
---
**(f)**
- **Sets Defined:**
- \( A = \{x \in \mathbb{R} \mid \cos(x) \in \mathbb{Z}\} \)
- \( B = \{x \in \mathbb{R} \mid \sin(x) \in \math
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