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(ft A = {Xxx || √ ² = x ² (for X₁ VER be a relation on R Reflexive yes or no yes or no yes or no symmetric Transistive

(ft A = {Xxx || √ ² = x ² (for X₁ VER be a relation on R Reflexive yes or no yes or no yes or no symmetric Transistive

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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**Mathematical Relations and Properties** Let \( A = \{ (x, y) | y^2 = x^2 \} \) for \( x, y \in \mathbb{R} \) Determine if this is a relation on \( \mathbb{R} \) that is: - Reflexive: Yes or No - Symmetric: Yes or No - Transitive: Yes or No **Explanation:** 1. **Reflexive**: A relation \( R \) is reflexive if for every element \( x \) in set \( A \), \( (x, x) \in R \). Here, check if for every real number \( x \), \( y^2 = x^2 \) holds true when \( y = x \). 2. **Symmetric**: A relation \( R \) is symmetric if whenever \( (x, y) \in R \), then \( (y, x) \in R \) as well. 3. **Transitive**: A relation \( R \) is transitive if whenever \( (x, y) \in R \) and \( (y, z) \in R \), then \( (x, z) \in R \) must also hold. Analyze the properties based on the definition of the relation \( A \).
Transcribed Image Text:**Mathematical Relations and Properties** Let \( A = \{ (x, y) | y^2 = x^2 \} \) for \( x, y \in \mathbb{R} \) Determine if this is a relation on \( \mathbb{R} \) that is: - Reflexive: Yes or No - Symmetric: Yes or No - Transitive: Yes or No **Explanation:** 1. **Reflexive**: A relation \( R \) is reflexive if for every element \( x \) in set \( A \), \( (x, x) \in R \). Here, check if for every real number \( x \), \( y^2 = x^2 \) holds true when \( y = x \). 2. **Symmetric**: A relation \( R \) is symmetric if whenever \( (x, y) \in R \), then \( (y, x) \in R \) as well. 3. **Transitive**: A relation \( R \) is transitive if whenever \( (x, y) \in R \) and \( (y, z) \in R \), then \( (x, z) \in R \) must also hold. Analyze the properties based on the definition of the relation \( A \).
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