**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]

If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

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

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