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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
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
**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:** There are no graphs or diagrams in this text.
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:** There are no graphs or diagrams in this 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. --- **(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
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. --- **(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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