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. Since R is symmetric and x R y, then y R x. Therefore, by definition of a symmetric relation, R is symmetric, and so the statement is true. Therefore, by definition of a symmetric relation, R is not symmetric, and so the statement is false. Then by definition of R-1, y R x. Since R is symmetric and y R x, then x R y. Then by definition of R-1, y R¬1 x. Then by definition of R, x R y. Then by definition of R-1, x R¬1 y. 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 y. 2. ---Select--- 3. --Select-- 4. ---Select--- 5. ---Select--
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. Since R is symmetric and x R y, then y R x. Therefore, by definition of a symmetric relation, R is symmetric, and so the statement is true. Therefore, by definition of a symmetric relation, R is not symmetric, and so the statement is false. Then by definition of R-1, y R x. Since R is symmetric and y R x, then x R y. Then by definition of R-1, y R¬1 x. Then by definition of R, x R y. Then by definition of R-1, x R¬1 y. 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 y. 2. ---Select--- 3. --Select-- 4. ---Select--- 5. ---Select--
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: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.
Since R is symmetric and x R y, then y R x.
Therefore, by definition of a symmetric relation, R is symmetric, and so the statement is true.
Therefore, by
nition of a symmetric relation, R is not symmetric, and so
statement is false.
Then by definition of R, y R x.
Since R is symmetric and y R x, then x R y.
Then by definition of R-1, y R¬1 x.
Then by definition of R, x R y.
Then by definition of R¯1, x R¬1 y.
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. --Select---
4. ---Select--
5. ---Select---
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