5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a) Write R as a subset of X X X. (b) Determine if R is reflexive, symmetric, antisymmetric, and/or transitive.
5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a) Write R as a subset of X X X. (b) Determine if R is reflexive, symmetric, antisymmetric, and/or transitive.
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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![5. Let \( X \) be the set \( X = \{1, 2, 3\} \), and let \( R \) be the relation defined on \( X \) by \( x_1 \, R \, x_2 \) if \( x_1 + x_2 \neq 3 \).
(a) Write \( R \) as a subset of \( X \times X \).
(b) Determine if \( R \) is reflexive, symmetric, antisymmetric, and/or transitive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F83e6d404-a58f-4813-89a1-cb0c2f763cb1%2Fab786648-6871-440d-9016-7557620e41a7%2F85lzrjd_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let \( X \) be the set \( X = \{1, 2, 3\} \), and let \( R \) be the relation defined on \( X \) by \( x_1 \, R \, x_2 \) if \( x_1 + x_2 \neq 3 \).
(a) Write \( R \) as a subset of \( X \times X \).
(b) Determine if \( R \) is reflexive, symmetric, antisymmetric, and/or transitive.
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