Q3. Let R be a relation on the set A = {1,2,3}, defined as follows: R = {(1,1), (1,2), (1,3), (2, 2), (2, 3), (3, 3), } Which one of the following statements is true? Only 1 statement is true. A. R is reflexive, antisymmetric, and transitive, but R is not symmetric. B. R is reflexive and symmetric, but R is not antisymmetric nor transitive. C. R antisymmetric and transitive, but R is not reflexive nor symmetric. D. R is reflexive, symmetric, and antisymmetric, but R is not transitive. E. R is an equivalence relation on A.

Q3. Let R be a relation on the set A = {1,2,3}, defined as follows: R = {(1,1), (1,2), (1,3), (2, 2), (2, 3), (3, 3), } Which one of the following statements is true? Only 1 statement is true. A. R is reflexive, antisymmetric, and transitive, but R is not symmetric. B. R is reflexive and symmetric, but R is not antisymmetric nor transitive. C. R antisymmetric and transitive, but R is not reflexive nor symmetric. D. R is reflexive, symmetric, and antisymmetric, but R is not transitive. E. R is an equivalence relation on A.

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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Question

Q3. Let R be a relation on the set A = {1, 2, 3}, defined as follows:
R = {(1,1), (1,2), (1,3), (2, 2), (2, 3), (3, 3), }
Which one of the following statements is true? Only 1 statement is true.
A. R is reflexive, antisymmetric, and transitive, but R is not symmetric.
B. R is reflexive and symmetric, but R is not antisymmetric nor transitive.
C. R antisymmetric and transitive, but R is not reflexive nor symmetric.
D. R is reflexive, symmetric, and antisymmetric, but R is not transitive.
E. R is an equivalence relation on A.

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