Define the following relations on A = {1,2,3,4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R₁ and R₂ are reflexive, simply enter 1, 2 as the answer. Ro= {(2, 1), (4,4), (2, 3), (2, 2), (3, 4), (1, 1)} R₁ = {(4,4), (1, 1), (3, 3), (2,)} R₂= {(3, 1), (3, 3), (2, 2), (1, 1), (1,3), (4,4)} R3 = {(1,2), (1,3), (4, 2), (4,1), (4,3), (4,4)} R₁ = {(2, 1), (4,4), (2, 3), (3, 4), (4,3), (1, 2), (3, 2)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric? 4) Which relations are transitive?
Define the following relations on A = {1,2,3,4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R₁ and R₂ are reflexive, simply enter 1, 2 as the answer. Ro= {(2, 1), (4,4), (2, 3), (2, 2), (3, 4), (1, 1)} R₁ = {(4,4), (1, 1), (3, 3), (2,)} R₂= {(3, 1), (3, 3), (2, 2), (1, 1), (1,3), (4,4)} R3 = {(1,2), (1,3), (4, 2), (4,1), (4,3), (4,4)} R₁ = {(2, 1), (4,4), (2, 3), (3, 4), (4,3), (1, 2), (3, 2)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric? 4) Which relations are 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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![Define the following relations on A = {1, 2, 3, 4]. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R₁ and
R₂ are reflexive, simply enter 1, 2 as the answer.
Ro= {(2, 1), (4,4), (2, 3), (2, 2), (3, 4), (1,1)}
R₁ = {(4,4), (1, 1), (3, 3), (2,)}
R₂ = {(3, 1), (3, 3), (2, 2), (1, 1), (1,3), (4,4)}
R3= {(1,2), (1, 3), (4, 2), (4, 1), (4,3), (4,4)}
R₁ = {(2, 1), (4,4), (2, 3), (3, 4), (4,3), (1, 2), (3, 2)}
1) Which relations are reflexive?
2) Which relations are symmetric?
3) Which relations are anti-symmetric?
4) Which relations are transitive?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8fabc15-e5db-480c-94d9-e42b67b656a8%2Fc4dcebe4-cefc-4771-acad-ce2405c334a2%2Ft8nn0p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Define the following relations on A = {1, 2, 3, 4]. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R₁ and
R₂ are reflexive, simply enter 1, 2 as the answer.
Ro= {(2, 1), (4,4), (2, 3), (2, 2), (3, 4), (1,1)}
R₁ = {(4,4), (1, 1), (3, 3), (2,)}
R₂ = {(3, 1), (3, 3), (2, 2), (1, 1), (1,3), (4,4)}
R3= {(1,2), (1, 3), (4, 2), (4, 1), (4,3), (4,4)}
R₁ = {(2, 1), (4,4), (2, 3), (3, 4), (4,3), (1, 2), (3, 2)}
1) Which relations are reflexive?
2) Which relations are symmetric?
3) Which relations are anti-symmetric?
4) Which relations are transitive?
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