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 acommon 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 integerx is divisible by an integer y with y # 0 if and only if there exists an integer k such thatx = yk.d. Ris a relation on Z* such that (x, y) E R if and only if there is a positive integer n suchthat 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.

Reflexive: Yes(x, x) belongs to R for all x in the set Anti-reflexive: NoIt is reflexive Symmetric:…

Reflexive. Transitive. • A partial order. • A strict order. • An equivalence relation. 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.

Reflexive. Transitive. • A partial order. • A strict order. • An equivalence relation. 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.

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

See similar textbooks

Related questions

Q: Let X = {0, 1}. (a) List (as subsets of X X X) all possible relations on X. This answer has not been…

Q: Define two sets: a letter set A = {t. p. c) and a word set B = {proposition, math, proof, discrete).…

Q: Suppose ρ is the relation defined on P({1, 2, 3}) in which, for A, B ∈ P({1, 2, 3}), AρB means "A…

A: Given: P({1, 2, 3}) A, B ∈ P({1, 2, 3}) AρB means "A and B both have exactly 2 elements." ρ is…

Q: Create a knowledge base using frames for the description of the domain given below. Arepresentation…

A: A knowledge base which refers to an organized collection of facts and that of the data about a…

Q: Given the relation U below, use ordered pair notation to express the relation U o U. U o U = { Ex:…

A: To express the relation UoU (composition of relations U and U), find all pairs (x, y) such that…

Q: 3. Given a relation R( A, B, C, D) where FDs ans CKs are such : FDs AB -> C, BC -> D, CD -> A CKs АB…

A: Here in this question we have given a relation R and we have asked to check highest normal form in…

Q: Let a bus timetable be represented by a list of routes where each route is repre- sented by…

A: I Have answered this question in step 2.

Q: Let R be a relation on A = {0, 2, 3, 7} and R = {(7,7), (3, 3), (0, 2), (2, 0), (2, 2), (0, 0)}. Are…

A: SOLUTION- Given, A ={0,2,37} and R={(7,7),(3,3),(0,2),(2,0),(2,2),(0,0)} 1)True A relation R…

Q: 3. Suppose the relation R1(A,B) and R2(B,C,D) have the following tuples: A 1 7 2 4 9 B A T G C T B…

A: A theta join connects tables based on a relationship other than the equality of two columns. A theta…

Q: Consider the relation R defined on the set Z x Z: R = {((a,b),(c,d)) | a = c (mod 4) a b = d (mod…

A: given that

Q: Given: Relation R = {(a,c), (b,c), (c,c)} and Set S = {a, b, c} %3D Complete Relation R to be…

A: Given: To make the relation R symmetric.

Q: Every aggregatic

A: Every aggregation relationship is an association Aggregation is a type of linkage between two or…

Q: Complete the following clojure program to add two new family relations (Niece and Nephew) as well as…

A: A collection of instructions written in the Clojure programming language is called a Clojure…

Q: 3. R is a binary relation over N, the set of natural integers. (x, y) € R iff x mod 7 = y mod 7. R…

A: Binary Relation:A binary relation is a mathematical concept that defines a relationship between two…

Q: Let the universe of discourse be the set of relations on the set A. Write the following English…

A: Given the universe of discourse be the set of relation on the set A. Let the universe of the…

Q: Given the relations U and S below, use ordered pair notation to express the relation So U. a b b

A: To express the relation SoU (composition of relations S and U), find all pairs (x, y) such that…

Q: Constructing a link such as second course may be done by starting with a number of connections that…

A: Introduction: Let's say we have a connection that was produced from a many-to-one relationship and…

Q: Given the following UML diagram: Student - studentID: String + getStudentID(): String + toString():…

A: Here is the java code of the above problem. See below step for code.

Q: Write in your own words description of following attributes of sets. Provide one example for each…

A: Defined the each attributes which are set Cardinality,Empty Set,Subset and Power Set

Q: Indicate the properties of each of the following relations. For each relation, indicate whether it…

A: here are the properties of each relation:R is reflexive, symmetric, and transitive.R is…

Q: For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2),…

A: Brief explanation about Reflexive, Symmetric and Transitive is presented here:-

Q: For non empty binary relation R={(a, a).(a, b),(b, a).(b, b).(c, C).(C, d).(d, C).(d, d)} on the set…

Q: Let R be the relation R = {(a, b) | a < b} on the set of integers. Find a) R-!. b) R.

A: a)R-1

Q: Explain principle of substitutability with suitable example?

A: Explain principle of substitutability with suitable example:

Q: Q6) Let A = Z, the set of all positive integers, and we define the relation R on A as: a Rb if and…

Q: Put into second Normal form where A,B, and C are prime attributes R (A, B, C, D, E, F, G, H, I, J)…

A: Answer is

Q: Can relationship exist if cardinality is reduced to zero. Provide reason and Explain with the help…

A: Relationship: For internal process reasons, a “quantity outstanding” price is related to every…

Q: Consider the relation schema R(A, B, C, D, E, F) with the following set of tional dependencies FDs F…

A: We are given a relation schema and it is decomposed into several schemas. We are going to find out…

Q: Compare and contrast the advantages and disadvantages of magnetic and solid-state secondary storage…

A: Solid-state secondary storage devices: SSDs offer quicker startup times, perform speedy file…

Q: lation R on a set S, defined as x R y if and only if y R x. This is an example of? a) reflexive…

A: Introduction: A relation R on a set S, defined as x R y if and only if y R x. This is an example…

Q: Consider the following Relation instance of Students: ID firstNamelastName GPA Address 123 Albertson…

A: Given: What will be the result of given SQL query? SELECT ID,firstName FROM Students WHERE…

Q: Oa.2

A: Here as we can see all vertices have self loop. Thus the relation is = . Also as we can see there…

Q: Define referential integrity constraints. I need the answer in short sentences thanks

A: Introduction of Integrity Constraints: Integrity means in Database to maintain the consistency and…

Q: Can renaming be pushed through join and selection—that is, which of the following algebraic laws…

A: SUMMARY: - Hence we discussed all the points.

Q: The reflexive and transitive closure of the relation A = {(0,1),(1,2)} on B = {0,1,2} is…

A: Here in this question we have given a relation on some set B. and we have asked to find the…

Q: Consider the relation R = {(a, d), (b, a), (b, c), (c, b), (c, c), (d, a)} on the set {a, b, c, d}.…

A: Below are the required answers :

Q: I. Reflexive II. Symmetric I. Transitive IV. Antisymmetric For each of the following tvpes of…

A: - The question wants to know that what categories fell under the partial , total and equivalence…

Q: Refer to image and answer correctly for upvote! (Automata and Computation)

A: An equivalence relation must satisfy three properties:1. Reflexivity: Every element is related to…

Q: write this in relation algebra: SELECT s.sname FROM student s, reservation r WHERE s.sid!=r.sid

A: SQL statement to relational algebra is written in step 2.

Q: whay decision can be achieved by a fuzzy relation?

A: Fuzzy decision-making requires the collection of single or multicriteria technologies to choose the…

Question

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions

If a set A has 7 elements, then the total number of possible relations on A is 27 27 277 72
• • Reflexive. Anti-reflexive. Symmetric. Anti-symmetric. Justify all your answers. • Transitive. • A partial order. • A strict order. • An equivalence relation.
7 PLEASE TYPE ONLY***
Part 1 Let R be an equivalence relation on A = {0, 2, 3, 5} and R= {(5,5), (0, 2), (3, 3), (2, 0), (2, 2), (0, 0)}. There are defined by R. Part 2 unique equivalence classes
a
CAN U HELP ME IN THIS ONE?
2.Consider relation R=(A,B,C,D) with the following FDs: B → C, C > D, and D A a. List all candidate keys of R. b. Is R in 3NF? BCNF? Justify your answer
3,
Using the functional dependencies of Exercise 7.6, compute the canonicalcover Fc.
An illustration of a super type/subtype connection. that disjoint rule is applicable?
Implement in Python / Java Algorithm: Testing for lossless (nonadditive) join property. Input: A universal relation R, a decomposition D = { R1, R2, R3, ….. Rm } of R, and a set F of functional dependencies. 1. Create an initial matrix S with one row i for each relation in Ri in D, and one column j for each attribute Aj in R. 2. Set S(i, j) := bij for all matrix entries. (* each bij is a distinct symbol associated with indices (i, j) * ) {for each column j representing attribute Aj {if (relation Ri includes attribute Aj ) then set S(I, j):=aj;};}; (* each aj is a distinct symbol associated with index (j) *) 3. For each row i representing relation schema Ri {for each functional dependency X → Y in F {for all rows in S which have the same symbols in the columns corresponding to attributes in X {make the symbols in each column that correspond to an attribute in Y be…
Consider the relation R on Z? given by: R = {((a, b), (c, d)) : a +d = c+b} Prove that R is an equivalence relation, and determine 3 elements of [(1,3)], the equivalence class of (1, 3).