Is the following statement true or false? If R is any symmetric relation on a set A, then R is symmetric. The statement is true Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order. Therefore, by definition of a symmetric relation, R-1 is symmetric, and so the statement is true. Therefore, by definition of a symmetric relation, R-1 is not symmetric, and so the statement is false. Then by definition of R, y Rx. Since R is symmetric and y R x, then x R y. Since R is symmetric and x R y, then y R x. Then by definition of R, x R-1 y. Then by definition of R-1, xR y. Then by definition of R1, y R-1 x. Proof: -1 1. Let R be any symmetric relation on a set A, and suppose that x and y are any elements of A such that x R y. 2. ---Select-- 3. Since R is symmetric and y Rx. then x Ry. 4. ---Select--- 5. Therefore, by definition of a symmetric relation, R1 is symmetric, and so the statement is true. Need Help? Read It
Is the following statement true or false? If R is any symmetric relation on a set A, then R is symmetric. The statement is true Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order. Therefore, by definition of a symmetric relation, R-1 is symmetric, and so the statement is true. Therefore, by definition of a symmetric relation, R-1 is not symmetric, and so the statement is false. Then by definition of R, y Rx. Since R is symmetric and y R x, then x R y. Since R is symmetric and x R y, then y R x. Then by definition of R, x R-1 y. Then by definition of R-1, xR y. Then by definition of R1, y R-1 x. Proof: -1 1. Let R be any symmetric relation on a set A, and suppose that x and y are any elements of A such that x R y. 2. ---Select-- 3. Since R is symmetric and y Rx. then x Ry. 4. ---Select--- 5. Therefore, by definition of a symmetric relation, R1 is symmetric, and so the statement is true. Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Is the following statement true or false?**
If \( R \) is any symmetric relation on a set \( A \), then \( R^{-1} \) is symmetric.
**The statement is:** true.
---
**Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order.**
1. Let \( R \) be any symmetric relation on a set \( A \), and suppose that \( x \) and \( y \) are any elements of \( A \) such that \( x \, R^{-1} \, y \).
2. Since \( R \) is symmetric and \( y \, R \, x \), then \( x \, R \, y \).
3. Since \( R \) is symmetric and \( x \, R \, y \), then \( y \, R \, x \).
4. By definition of \( R^{-1} \), \( x \, R^{-1} \, y \).
5. Therefore, by definition of a symmetric relation, \( R^{-1} \) is symmetric, and so the statement is true.
---
**Proof:**
1. Let \( R \) be any symmetric relation on a set \( A \), and suppose that \( x \) and \( y \) are any elements of \( A \) such that \( x \, R^{-1} \, y \).
2. \( x \, R^{-1} \, y \).
3. Since \( R \) is symmetric and \( y \, R \, x \), then \( x \, R \, y \).
4. Therefore, by definition of a symmetric relation, \( R^{-1} \) is symmetric, and so the statement is true.
**Need Help?** [Read it]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcc357075-d330-4116-93bc-b2819b26405c%2Fb5451b84-3241-4492-ab54-d69779306f8a%2Fs27gx2m_processed.png&w=3840&q=75)
Transcribed Image Text:**Is the following statement true or false?**
If \( R \) is any symmetric relation on a set \( A \), then \( R^{-1} \) is symmetric.
**The statement is:** true.
---
**Construct a proof for your answer by selecting sentences from the following scrambled list and putting them in the correct order.**
1. Let \( R \) be any symmetric relation on a set \( A \), and suppose that \( x \) and \( y \) are any elements of \( A \) such that \( x \, R^{-1} \, y \).
2. Since \( R \) is symmetric and \( y \, R \, x \), then \( x \, R \, y \).
3. Since \( R \) is symmetric and \( x \, R \, y \), then \( y \, R \, x \).
4. By definition of \( R^{-1} \), \( x \, R^{-1} \, y \).
5. Therefore, by definition of a symmetric relation, \( R^{-1} \) is symmetric, and so the statement is true.
---
**Proof:**
1. Let \( R \) be any symmetric relation on a set \( A \), and suppose that \( x \) and \( y \) are any elements of \( A \) such that \( x \, R^{-1} \, y \).
2. \( x \, R^{-1} \, y \).
3. Since \( R \) is symmetric and \( y \, R \, x \), then \( x \, R \, y \).
4. Therefore, by definition of a symmetric relation, \( R^{-1} \) is symmetric, and so the statement is true.
**Need Help?** [Read it]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
