2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3, 3)} R2 = {(3,3), (1, 1), (4, 4), (7, 4), (7, 7), (4, 7), (7, 3)} • R3 = {(3,3), (7,7), (1, 7), (4, 4), (7, 4), (1, 1), (1, 4)} • R4 = {(7,3), (3, 3), (1, 1), (4, 4), (7, 7), (3, 1), (1,3), (3, 7)} %3D (a) Which of these relations are reflexive? If not, give a counterexample. (b) Which of these are symmetric? If not, give a counterexample. (c) Which of these are anti-symmetric? If not, give a counterexample. (d) Which of these are transitive? If not, give a counterexample. (e) Which of these are partial ordering? If not, explain why not. (f) Which of these are equivalence relations? If not, explain why not. (g) Draw the digraph of R4. (h) R2 o R4 =
2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3, 3)} R2 = {(3,3), (1, 1), (4, 4), (7, 4), (7, 7), (4, 7), (7, 3)} • R3 = {(3,3), (7,7), (1, 7), (4, 4), (7, 4), (1, 1), (1, 4)} • R4 = {(7,3), (3, 3), (1, 1), (4, 4), (7, 7), (3, 1), (1,3), (3, 7)} %3D (a) Which of these relations are reflexive? If not, give a counterexample. (b) Which of these are symmetric? If not, give a counterexample. (c) Which of these are anti-symmetric? If not, give a counterexample. (d) Which of these are transitive? If not, give a counterexample. (e) Which of these are partial ordering? If not, explain why not. (f) Which of these are equivalence relations? If not, explain why not. (g) Draw the digraph of R4. (h) R2 o R4 =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 19E
Related questions
Question
![2. For each of the following relations on the set {1,3,4,7}.
• R1 = {(7, 7), (1, 1), (4, 4), (3, 3)}
• R2
{(3, 3), (1, 1), (4, 4), (7, 4), (7, 7), (4, 7), (7, 3)}
• R3 = {(3,3), (7, 7), (1, 7), (4, 4), (7, 4), (1, 1), (1, 4)}
• R4 = {(7,3), (3, 3), (1, 1), (4, 4), (7, 7), (3, 1), (1, 3), (3, 7)}
(a) Which of these relations are reflexive? If not, give a counterexample.
(b) Which of these are symmetric? If not, give a counterexample.
(c) Which of these are anti-symmetric? If not, give a counterexample.
(d) Which of these are transitive? If not, give a counterexample.
(e) Which of these are partial ordering? If not, explain why not.
(f) Which of these are equivalence relations? If not, explain why not.
(g) Draw the digraph of R4.
(h) R2 o R4 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F404d1ef0-3316-4381-9a29-8161054821c1%2F0a758a17-9663-410e-9e10-4fa35dff9374%2F8x78dn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. For each of the following relations on the set {1,3,4,7}.
• R1 = {(7, 7), (1, 1), (4, 4), (3, 3)}
• R2
{(3, 3), (1, 1), (4, 4), (7, 4), (7, 7), (4, 7), (7, 3)}
• R3 = {(3,3), (7, 7), (1, 7), (4, 4), (7, 4), (1, 1), (1, 4)}
• R4 = {(7,3), (3, 3), (1, 1), (4, 4), (7, 7), (3, 1), (1, 3), (3, 7)}
(a) Which of these relations are reflexive? If not, give a counterexample.
(b) Which of these are symmetric? If not, give a counterexample.
(c) Which of these are anti-symmetric? If not, give a counterexample.
(d) Which of these are transitive? If not, give a counterexample.
(e) Which of these are partial ordering? If not, explain why not.
(f) Which of these are equivalence relations? If not, explain why not.
(g) Draw the digraph of R4.
(h) R2 o R4 =
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