5. Determine whether the relation with the directed graph is an equivalence relation:

Answered: Image /qna-images/answer/142fbf1b-67f8-4f61-8e61-01eb356f29a2.jpg

Answered: Determine whether the relation with the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Similar questions

Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
20 - Determine whether the relation with the directed graph shown is an equivalence relation ? a b d a) O Yes b) O No
Identify the directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)}.
(c). Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum number of ordered pairs which when added to R make it an equivalence relation?Discuss your reasoning.
Define: what is an equivalence relation?
Check the following if it is equivalence relation or partial ordering.
For the following directed graph, do the following: 1. give (in set notation, e.g. { (a,b), (c,x), ...}) the set that corresponds to the graph expressed as a relation (set of ordered pairs). (8 pts) 2. is the relation reflexive? (2 pts) Why or why not? 3. is the relation symmetric? (2 pts) Why or why not? 4. is the relation transitive? (4 pts) Why or why not? a b d e
For each of the following relations, determine whetheri) it is an equivalence relation. Why or why not? Explain.ii) it is a partial order. Why or why not? Explain.Note: If you claim that a relation has a specific property which makes it a partial order or an equivalencerelation, please explain why you think that the relation has the claimed property. For example, if you claimthat a relation is symmetric, you should explain why you think that the relation is symmetric. Follow thesame line of argument for all properties. Give examples and/or counterexamples when needed. 1) Let R be a relation on N × N where (a, b) R (c, d) if a ≤ c and b ≥ d
Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here. Is the relation transitive? Explain why or why not.
Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here. Is the relation reflexive? Explain why or why not.
Give small examples of equivalence relations R and P such that RUP is not an equivalence relation.

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