For each of the following relations, determine whether the relation is:(i) Reflexive.(ii) Anti-reflexive.(iii) Symmetric.(iv) Anti-symmetric.(v) Transitive.(vi) A partial order.(vii) A strict order.(viii) An equivalence relation.Justify all your answers. You need to have eight answers for each question.a The domain of R is a group of students. Ry if x has earned more credits than y. (NOTE: You canassume there are at least two students who have not earned the same number of credits.)b R is a relation on Z such that Ry if and only if x - y = 3m for some integer m.c The domain R is the set of all cell phone towers in a network. Two towers can communicate if theyare within a distance of three miles from each other. Ry if x can communicate with y. (NOTE: Youcan assume that there are at least two towers that are within three miles of each other.)

Subject: Discrete MathematicsSub-subject: Relations and their PropertiesTopic: Properties of…

Answered: For each of the following relations,…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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For each of the following relations, determine whether the relation is: • Transitive. • A partial order. • A strict order. • An equivalence relation. Reflexive. Anti-reflexive. Symmetric. • Anti-symmetric. Justify all your answers. a. Ris a relation on the set of all people such that (a, b) e R if and only if a and b have a common grandparent. b. Ris a relation on Z such that (x, y) E R if and only if |x – y| < 2. c. Ris a relation on Z* such that (x, y) E R if and only if x is divisible by y. Hint: An integer x is divisible by an integer y with y # 0 if and only if there exists an integer k such that x = yk. d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n such that x" = y. e. Ris a relation on Z x Z such that ((a, b), (c, d)) E R if and only if a < c and b < d.
Indicate the properties of each of the following relations. For each relation, indicate whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, and/or transitive. You do not need to justify your answer. 1. R is a relation on set Z such that (x, y) E R if and only if x + y = 0. 2. R is a relation on set Z such that (x, y) ER if and only if x and y have opposite parity. Hint: Two integers have opposite parity if one is even and the other one is odd.
Let R be a relation on A = {0, 2, 7, 8} and R = {(7, 2), (8, 8), (8, 0), (2, 7), (2, 2), (7,0)}. Are the following statements true or false? 1. R is an equivalence relation ? ? ? ? ? ? V 2. R is reflexive ✓ 3. R is transitive 4. R is anti-symmetric 5. R is a partial order 6. R is symmetric
Give all the keys of R if the functional dependencies on R in each of the following cases
We studied different properties of relations like reflexive, symmetric, antisymmetric, transitive. Please provide one example relation each for each property of the relation. Try to come up with original examples which can be seen practically. (Example, Reflexive relation R = {(a, b) | a and b share same birthday}, Symmetric relation R = {(a, b) | a and b are friends}, Antisymmetric relation R = {(a, b) | a is instructor of b}, Transitive relation R = {(a, c) | a is sibling of b, b is sibling of c, then a is sibling of c}
Computer Science Match each of the following relations on S = {the set of all people in the US} with the correct category. Your answer should include all properties that apply to the relation. xρy ↔ x is the husband of y [ Choose ] Reflexive Symmetric Reflexive and Symmetric Transitive None Symmetric and Transitive xρy ↔ x has the same parents as y [ Choose ] Reflexive Symmetric Reflexive and Symmetric Transitive None Symmetric and Transitive xρy ↔ x is the spouse of y [ Choose ] Reflexive Symmetric Reflexive and Symmetric Transitive None Symmetric and Transitive xρy ↔ x is a brother of y [ Choose ] Reflexive Symmetric Reflexive and Symmetric Transitive None Symmetric and Transitive
9.. Don't explain ... just tell me which is right... solve only if you are 100% sure
Consider the following five relations on the set A = {1, 2, 3, 4}. Determine which of the * .relations are reflexive R2 = {(1, 1)(1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} R4 = A x A R1 = {(1, 1), (1, 2), (2, 3), (1, 3), (4, 4)} R3 = {(1, 3), (2, 1)}
whay decision can be achieved by a fuzzy relation?
2. Let N be a relation on R where Ny if and only if zy < 0. Is N reflexive? Is N symmetric? Is N transitive? Prove or provide a counterexample for each of these three properties.
let X = {0, 1}
Question 3 • Let A be the set A={a,b,c,d} and R is a relation on set A, where R = { (a,a), (a,b) ,(b,a),(b,b), (c,d),(c,c) ,(d,d)} Determine if R is a reflexive and symmetric relation on A.

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