Let A = {1, 2, 3, 4}. Prove or disprove each of the following statements. If the statement is true, you must simply describe the relation you choose as a subset of A x A and draw its directed graph (arrow diagram). If the statement is false, then you must explain (prove) why there exists no such relations. (a) There exists a relation R on A so that R is reflexive and symmetric, but R is not antisymmetric nor transitive. (b) There exists a relation S on A so that S is symmetric and transitive, but S is not antisymmetric nor reflexive. (c) There exists a relation T on A so that T is antisymmetric and transitive, but T is not symmetric nor reflexive.
Let A = {1, 2, 3, 4}. Prove or disprove each of the following statements. If the statement is true, you must simply describe the relation you choose as a subset of A x A and draw its directed graph (arrow diagram). If the statement is false, then you must explain (prove) why there exists no such relations. (a) There exists a relation R on A so that R is reflexive and symmetric, but R is not antisymmetric nor transitive. (b) There exists a relation S on A so that S is symmetric and transitive, but S is not antisymmetric nor reflexive. (c) There exists a relation T on A so that T is antisymmetric and transitive, but T is not symmetric nor reflexive.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
Related questions
Question
How do you deal with part(c) and part (d),I also need the directed graph
Transcribed Image Text:1. Let A = {1, 2, 3, 4}. Prove or disprove each of the following statements. If the statement is
true, you must simply describe the relation you choose as a subset of A x A and draw its
directed graph (arrow diagram). If the statement is false, then you must explain (prove) why
there exists no such relations.
(a) There exists a relation R on A so that R is reflexive and symmetric, but R is not
antisymmetric nor transitive.
(b) There exists a relation S on A so that S is symmetric and transitive, but S is not
antisymmetric nor reflexive.
(c) There exists a relation T on A so that T is antisymmetric and transitive, but T is not
symmetric nor reflexive.
(d) There exists a relation U on A so that U is symmetric and antisymmetric, but U is not
transitive.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning