Define the following relations on A = {5,6,7,9). 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), (7,7), (9,9), (6,6)} R₁ = {(5,5), (7,6), (7, 7), (7, 9), (9, 6), (6, 6), (9,9)} R₂ = {(9,9), (7, 7), (6, 9), (5, 5), (6, 6), (9,5), (9,6)} R3 = {(7,9), (5,5), (6, 6), (7, 7), (9,9)} RA= {(9,9), (5,5), (5,9), (7, 9), (7,5), (6, 6), (9,5), (7,7), (5,7)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Define the following relations on A = {5, 6, 7, 9). 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), (7,7), (9,9), (6,6)}
R₁ = {(5,5), (7,6), (7, 7), (7, 9), (9, 6), (6, 6), (9,9)}
R2 = {(9,9), (7,7), (6, 9), (5, 5), (6, 6), (9,5), (9,6)}
R3 = {(7,9), (5,5), (6, 6), (7, 7), (9,9)}
R₁ = {(9,9), (5,5), (5,9), (7, 9), (7,5), (6, 6), (9,5), (7, 7), (5,7)}
1) Which relations are reflexive?
2) Which relations are symmetric?
3) Which relations are anti-symmetric?
4) Which relations are transitive?
Transcribed Image Text:Define the following relations on A = {5, 6, 7, 9). 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), (7,7), (9,9), (6,6)} R₁ = {(5,5), (7,6), (7, 7), (7, 9), (9, 6), (6, 6), (9,9)} R2 = {(9,9), (7,7), (6, 9), (5, 5), (6, 6), (9,5), (9,6)} R3 = {(7,9), (5,5), (6, 6), (7, 7), (9,9)} R₁ = {(9,9), (5,5), (5,9), (7, 9), (7,5), (6, 6), (9,5), (7, 7), (5,7)} 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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