Define the following relations on A = {2, 4, 5, 7}. 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= {(5,5), (7,5), (5, 4), (7, 7), (2, 2), (4, 5), (4, 4), (4,7), (5, 7)} R₁ = {(4,7), (4,4), (7, 2), (5, 5), (2, 2), (4, 2), (7, 7)} R2 {(5,5), (4,4), (2, 2), (7, 7), (4,7)} R3 = {(5,5), (4,4), (7, 7), (2, 2)} R4 = {(4,4), (2, 2), (5, 5), (2, 7), (7, 2), (7,5), (7, 7)} 1) Which relations are re = e? 2) Which relations are symmetric? 3) Which relations are anti-symmetric?
Define the following relations on A = {2, 4, 5, 7}. 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= {(5,5), (7,5), (5, 4), (7, 7), (2, 2), (4, 5), (4, 4), (4,7), (5, 7)} R₁ = {(4,7), (4,4), (7, 2), (5, 5), (2, 2), (4, 2), (7, 7)} R2 {(5,5), (4,4), (2, 2), (7, 7), (4,7)} R3 = {(5,5), (4,4), (7, 7), (2, 2)} R4 = {(4,4), (2, 2), (5, 5), (2, 7), (7, 2), (7,5), (7, 7)} 1) Which relations are re = e? 2) Which relations are symmetric? 3) Which relations are anti-symmetric?
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:Define the following relations on A = {2, 4, 5, 7}. 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 = {(5,5), (7, 5), (5, 4), (7, 7), (2, 2), (4, 5), (4, 4), (4, 7), (5, 7)}
R₁ = {(4,7), (4,4), (7, 2), (5, 5), (2, 2), (4,2), (7, 7)}
R₂ = {(5,5), (4, 4), (2, 2), (7, 7), (4,7)}
R3 = {(5,5), (4,4), (7, 7), (2, 2)}
R₁ = {(4,4), (2, 2), (5, 5), (2, 7), (7, 2), (7,5), (7,7)}
1) Which relations are reflexive?
2) Which relations are symmetric?
3) Which relations are anti-symmetric?
4) Which relations are transitive?
5) Which relations are equivalence relations?
6) Which relations are partial orders?
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