Exercise 8.9.1: Recognizing equivalence relations. Determine whether each relation is an equivalence relation. Justify your answer. If the relation is an equivalence relation, then describe the partition defined by the equivalence classes. (c) The domain is a group of people. Person x is related to person y under relation S if x is currently the spouse of person y. You can assume that there is no polygamy and that there is at least one person who is married to another person in the group.

Q: Determine whether the relation R on the set of all real numbers is reflexive, symmetric and/or…

A: (a) A = Set of all real numbersR = {(x, y) |x + y = 0} The relation R is not reflexive, because x +…

Q: Match each of the following relations on S = {the set of all people in the US} with the correct…

A: Small Example to understand Reflexive, Symmetric, and Transitive: - s={1,2,3,4} R={(1,1)…

Q: The relation "=" based on the two relations ≤ and > a = b if and only if a ≤ b and a ≥ b Formulate…

A: Introduction:  Relations are used to describe how elements of a set are related to one another,…

Q: 3. Disprove the following rule: {B > CD, AB → E, E → C} |= {AE → CD} To disprove a rule, construct a…

A:

Q: Exercise 3.2.1: Consider a relation with schema R(A, B, C, D) and FD’s AB → C, C → D, and D → A. a)…

A: Answer : For the single attributes we have {A}+= A, {B}+= B, {C}+= ACD, and {D}+=AD. Thus, the only…

Q: Consider the representation of the ternary relationship of Figure 6.29a usingthe binary…

A: The following given is the simple instance of E, A, B, C, RA, RB, and RC that cannot correspond to…

Q: Find a minimal cover in a standard form for the relation schema R(A, B,C, D, E, F, G, H) with the…

A: A minimal cover or canonical cover means a minimum set of functional dependencies. A canonical cover…

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: SIf a decomposition of a relation R into R¡ and R2 is lossless, then which of the followings are…

A: If a decomposition of a relation “R” into “R1”, and “R2” is lossless then it produces “R” by…

Q: 2. Relation R(a,b) contains the following tuples: (1,2), (1,3), (1,4), (2,3), (3,4). and (4,5).…

A: The Answer is in Below Steps

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: If aRb ånd bRc together imply cRa. Which of the following options is/are correct? (a) If a relation…

A: The answer is

Q: Consider a relation schema R = (X, Y, Z) on which the following functional dependencies hold: {XY-Z,…

A:

Q: Question 1: FDs and Keys (a) Consider a relation schema R(A, B, C, D, E), and the set of…

A: Here in this question we have given a relation R. And also given set of functional dependenciesF =…

Q: Consider the following relation: R (A, B, C, D, E, F) You are given the following list of functional…

A:

Q: c) Find Un V. d) Find T-S.

A: The intersection of two sets A and B, denoted by A∩B, consists of all elements that are both in A…

Q: A decomposition of a relation R into Rị and R2 is dependency preserving, if - (a) R can be…

A: Answer: The correct option is “(d) All of them”

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: Assume we have two relations R(a,b) and S(b,c). All three attributes (a, b, and c) are integer…

A: Lets see the solution in the next steps

Q: Consider a relation consisting of the attributes A, B, C, with the following set of functional…

A:

Q: Which of these FDs hold on the

A: Functional dependency: The columns of a relational table are functionally dependent on another…

Q: Consider a relation schema R = (X, Y, Z) on which the following functional dependencies hold: {XY →…

A: Here in this question we have given a relation schema R = (X, Y, Z) on which the following…

Q: This question concerns the logical design of a relation schema LOAN describing the borrowing of a…

A: The relation schema:- LOAN(catalogNo, dateOut, memberNo, dateReturn)

Q: 2. Let R be the binary relation on A= {a, b, c} with the graphical representation shown below: a…

A: To check reflexive, symmetric and transitive nature of graph.

Q: D={0,1}^6. The following relation has the domain D. Is the following an equivalence relation?…

A: An equivalence relation is a binary relation on a set that satisfies three properties: reflexivity,…

Q: Select all binary relation properties that apply to the following relation: Equal magnitude: |x| =…

A: An algorithm is a stepwise that procedure is  for solving a specific problem in a  number of steps.…

Q: Let R be an equivalence relation on A = {0,2,3,5} and R = {(5,5), (0, 2), (3, 3), (2, 0), (2, 2),…

A: To find the number of unique equivalence classes defined by R, we need to determine the number of…

Q: For the following relations on the set of college students, determine if it satisfies each of the…

A: In this question, it is asked to state which the given statement is reflexive, transitive,…

Q: A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if…

A: I have provided solution in step2

Q: Consider the universal relation: R = (A, B, C, D, E, F, G, H, I, J) and the set of functional…

A: A crucial step in relational database architecture is database normalization, which entails breaking…

Intermediate SQL Concepts

A query is a request for data or information from one or more database tables. This information could be presented in the form of pictorials, graphs, or complicated findings which helps in easy interpretation. Structured Query Language (SQL) is the most widely used programming language for retrieving and organizing data from relational databases. Collection of tables with rows and columns is referred to as a database. SQL is the language of databases. It makes it easier to extract specific data from databases, which can then be used for analysis.