For the binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to b, which of the following statements would be true?R={ (0,4), (1, 1), (1, 3), (1, 4), (2, 1), (2, 2), (3, 2), (4, 4) }where A = {0, 1,2, 3, 4}Select one:O Ris symmetric but not antisymmetricO Ris antisymmetric but not symmetricO Ris both symmetric and antisymmetricO none of these optionsO Ris neither symmetric nor antisymmetric Which of the following definitions for the relation R (defined below) on A would constitute an equivalence relation?(n.b., Each tuple (a, b) in a given relation indicates that a is related to b, and A = {0,1, 2, 3, 4})Select one:O R={ (0,1), (0, 3), (1, 0), (2, 1), (2, 2), (2, 4), (3, 0), (3, 2), (3, 4), (4, 2), (4, 3) }O R={(0,0), (1,1), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4) }O none of these optionsO R={(0,0), (1, 4), (2, 0), (3, 0), (3, 4), (4, 0), (4, 3), (4, 4) }O R={(0,2), (0, 3), (0, 4), (1, 1), (1, 3), (2, 0), (2, 1),(2, 2), (2, 4), (3, 0), (3, 1), (4, 2), (4, 3), (4, 4) }O R={(0,0), (0, 1), (0, 3), (0, 4), (1, 2), (2, 1), (2, 2), (3, 4), (4, 2), (4, 4) }O R={ (0,1), (0, 2), (1, 3), (2,0), (2, 2), (3, 2), (3, 3), (4, 0), (4, 1), (4, 3), (4, 4) }

Answered: Image /qna-images/answer/d29be6c6-6ac1-45b3-9c0f-e6f3f148330d.jpg

Which of the following definitions for the relation R (defined below) on A would constitute an equivalence relation? (n.b., Each tuple (a, b) in a given relation indicates that a is related to b, and A = {0, 1, 2, 3, 4}) Select one: оR3{(0,1), (0, 3), (1,0), (2, 1), (2, 2), (2, 4), (3, 0), (3, 2), (3, 4), (4, 2), (4, 3)} оR3{ (0,0), (1,1), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4) } O none of these options O R={(0,0), (1, 4), (2, 0), (3, 0), (3, 4), (4, 0), (4, 3), (4, 4) } O R={(0,2), (0, 3), (0, 4), (1, 1), (1, 3), (2, 0), (2, 1), (2, 2), (2, 4), (3, 0), (3, 1), (4, 2), (4, 3), (4, 4) } O R={ (0,0), (0, 1), (0, 3), (0, 4), (1, 2), (2, 1), (2, 2), (3, 4), (4, 2), (4, 4) } O R={ (0,1), (0, 2), (1, 3), (2, 0), (2, 2), (3, 2), (3, 3), (4, 0), (4, 1), (4, 3), (4, 4) }

Which of the following definitions for the relation R (defined below) on A would constitute an equivalence relation? (n.b., Each tuple (a, b) in a given relation indicates that a is related to b, and A = {0, 1, 2, 3, 4}) Select one: оR3{(0,1), (0, 3), (1,0), (2, 1), (2, 2), (2, 4), (3, 0), (3, 2), (3, 4), (4, 2), (4, 3)} оR3{ (0,0), (1,1), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4) } O none of these options O R={(0,0), (1, 4), (2, 0), (3, 0), (3, 4), (4, 0), (4, 3), (4, 4) } O R={(0,2), (0, 3), (0, 4), (1, 1), (1, 3), (2, 0), (2, 1), (2, 2), (2, 4), (3, 0), (3, 1), (4, 2), (4, 3), (4, 4) } O R={ (0,0), (0, 1), (0, 3), (0, 4), (1, 2), (2, 1), (2, 2), (3, 4), (4, 2), (4, 4) } O R={ (0,1), (0, 2), (1, 3), (2, 0), (2, 2), (3, 2), (3, 3), (4, 0), (4, 1), (4, 3), (4, 4) }

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

For the binary relation R (defined below) on A and each tuple (a, b) indicating that a is related to b, which of the following statements would be true?
R={ (0,4), (1, 1), (1, 3), (1, 4), (2, 1), (2, 2), (3, 2), (4, 4) }
where A = {0, 1,2, 3, 4}
Select one:
O Ris symmetric but not antisymmetric
O Ris antisymmetric but not symmetric
O Ris both symmetric and antisymmetric
O none of these options
O Ris neither symmetric nor antisymmetric

Which of the following definitions for the relation R (defined below) on A would constitute an equivalence relation?
(n.b., Each tuple (a, b) in a given relation indicates that a is related to b, and A = {0,1, 2, 3, 4})
Select one:
O R={ (0,1), (0, 3), (1, 0), (2, 1), (2, 2), (2, 4), (3, 0), (3, 2), (3, 4), (4, 2), (4, 3) }
O R={(0,0), (1,1), (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4), (4, 2), (4, 3), (4, 4) }
O none of these options
O R={(0,0), (1, 4), (2, 0), (3, 0), (3, 4), (4, 0), (4, 3), (4, 4) }
O R={(0,2), (0, 3), (0, 4), (1, 1), (1, 3), (2, 0), (2, 1),
(2, 2), (2, 4), (3, 0), (3, 1), (4, 2), (4, 3), (4, 4) }
O R={(0,0), (0, 1), (0, 3), (0, 4), (1, 2), (2, 1), (2, 2), (3, 4), (4, 2), (4, 4) }
O R={ (0,1), (0, 2), (1, 3), (2,0), (2, 2), (3, 2), (3, 3), (4, 0), (4, 1), (4, 3), (4, 4) }

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