Module 2 : Entity-Relationship Model 15

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1 Module 2 : Entity-Relationship Model 15 Module-02 Entity Relationship Data Model 2.1 Motivation Data modeling is an essential step in the process of creating any Database Application. It helps Database designers understand the domain and organize their work accordingly. Database designing is crucial to high performance database system. Apart from improving the performance, properly designed database are easy to maintain, improve data consistency and are cost effective in terms of disk storage space. Data models define how the logical structure of a database is modeled. 2.2 Objective The main goal of this topic is to understand the data modeling as a first step for designing a database which provides the foundation for development of relational database structure. 2.3 Syllabus Prerequisites Syllabus Duration Self study Conceptual Modeling of a database Introduction to Data Modeling & Benefits Types of Data Models, The Entity-Relationship (ER) Model Object classes and The Entity-Relationship (ER) Model Notations, Attributes, and Keys Relationship Types, Relationship Sets, Entity Types 9 hours. 5 hours Step by step approach for designing an ER Model Generalization, Specialization and Aggregation Extended Entity-Relationship (EER) Model. 2.4 Definition: 1) Data Model- is a Conceptual tool used to describe: Data Data relationships Data semantics 2) Entity- is an object that exists and is distinguishable from other objects. Example: specific person, company, event, plant 3) Attribute - Is property of entity. Example: people have names and addresses 4) Entity set - Is a set of entities of the same type that share the same properties.

2 Database Management System 16 Example: set of all persons, companies, trees, holidays 5) Domain the set of permitted values for each attribute 6) Relationship - is an association among several entities 7) ER model:it is the pictorial representation of database in understandable format. 8) Specialization- is the process of defining one or more subclasses of a superclass by identifying its distinguishing characteristics. Unlike generalization, specialization is thus a top-down approach. It starts with the general entity (superclass) and forms specialized entity types (subclasses) based on specialized attributes or relationships specific to a subclass. 9) Generalization- is the process of defining general entity types from a set of specialized entity types by identifying their common characteristics. Generalization is a bottom-up approach as it starts with the specialized entity types (subclasses) and forms a generalized entity type (superclass). 10) Enhanced Entity-Relationships (EE-R) model -is a revised E-R model that extends the original E-R model and supports additional semantic concepts by providing new modeling constructs. 11) Superclass - is an entity type that has one or more distinct sub groups with unique attributes. 12) Subclass - is an entity type that shares common attributes or relationships distinct from other Subclasses. 13) Attribute Inheritance - is the property by which subclass entities inherit attributes of the superclass. The subclass entity type is an entity type in itself with a set of attributes and relationships. 14) Subclass Relationship - each subclass possesses attributes and relationships of its superclass, It can have its own attributes and relationships that distinguish one subclass from another the relationship between a superclass and subclass is always a one-to-one relationship. 15) Participation constraints - dictate whether each instance (member) of a superclass must participate as an instance (member) of a subclass. A participation of superclass instance may be mandatory or optional in one or more subclasses 16) Total Participation Rule - In total participation, membership is mandatory. Each instance of a superclass must be an instance of at least one subclass. 17) Partial Participation Rule - Membership is optional in a partial participation. An instance of a superclass does not have to be an instance of any of the subclasses. 18) Disjoint constraints define whether it is possible for an instance of a superclass to simultaneously be a member of one or more subclasses. Disjoint constraints indicate whether a superclass instance can be disjointed or overlap more than one subclass. 19) Disjoint Rule The disjoint rule states that if an instance of a superclass is a member of any subclass, then it cannot be a member of more than one subtype 20) Overlap Rule The overlap rule states that if an instance of a superclass is a member of any subclass, then it can be a member (overlap) of more than one subtype.

3 Module 2 : Entity-Relationship Model 17 21) Subclass Discriminator: The participation and disjoint constraints allow an instance of a superclass to be a member of one or more subclasses. We keep track of membership using a special attribute of a superclass,a subclass discriminator 2.5 Course Objective, Outcome and Learning outcome CO2: CO2: To give a good formal foundation on the relational model of data and usage of Relational Algebra Student should be able to design conceptual models of a database using ER modeling for real life applications and also construct queries in Relational Algebra. LO: After Completion of this module, student should be able to learn the following points Types of data models for database. Basic constructs of E-R Modeling The significance of the ER-model for DB design. How to develop ER-diagrams (schemas in the ER-model) for a given (small) application. 2.6 Module theory Notations: DB: Database DBMS: Database Management System E-R: Entity Relationship Introduction to Data Modeling: A Data Model is a logical structure of Database. Data model is a conceptual tool used to describe data and data relationships, data semantics and consistency constraints.there are two types of data models: 1. Object-based data models and 2. Record -based data models. Object Based Data Models Object based data models use concepts such as entities, attributes, and relationships. An entity is a distinct object (a person, place, concept, and event) in the organization that is to be represented in the database. Example is Entity-Relationship Model. Entity-Relationship Model: The ER model defines the conceptual view of a database. It works around real-world entities and the associations among them. At view level, the ER model is considered a good option for designing databases. An Entity-Relationship Model is based on Entities and their attributes.

4 Database Management System 18 Relationships among entities. We graphically display an E-R model using an entity-relationship diagram (or E-R diagram) like the sample in Figure 2.1. Fig Entity Relationship Model Entity An entity is a real-world entity having properties. In above example, Student and Class are considered as entities. Relationship Relationship is the logical association among entities. For Example, Enroll is relationship between Student and Class. Attributes - Attributes describe properties of entities and relationships. For Example Student entity has attributes such as stuid, firstname,lastname, major and credits Every attribute is defined by its set of values called domain. Record -based data models: 1. Hierarchical data model: In hierarchical model, data is organized into a tree like structure with each record is having one parent record and many children. At the top of hierarchy there is only one entity which is called Root. The data is stored as records which are connected to one another through links. A record is a collection of fields, with each field containing only one value. Fig Hierarchical data model

5 Module 2 : Entity-Relationship Model Network Data model: The network model is a database model conceived as a flexible way of representing objects and their relationships. In the network model, entities are organized in a graph, in which some entities can be accessed through several paths. Fig Hierarchical data model 3. Relational data Model: Relational data model is the primary data model, which is used widely around the world for data storage and processing. This model is simple and it has all the properties and capabilities required to process data with storage efficiency. In relational model, the data and relationships are represented by collection of inter-related tables. Each table is a group of column and rows, where column represents attribute of an entity and rows represents records. Fig Relational data Model

6 Database Management System 20 Comparison between Records -based data models: Characteristic Hierarchical model Network model Relational model Data structure Data manipulation Data integrity One to many or one to one relationships Based on parent child relationship Does not provide an independent stand alone query interface retrieve algorithms are complex and asymmetric Cannot insert the information of a child who does not have any parent. Multiple occurrences of child records which lead to problems of inconsistency during the update operation Deletion of parent results in deletion of child records Allowed the network model to support many to many relationships A record can have many parents as well as many children. CODASYL (Conference on Data Systems Languages) Retrieve algorithms are complex and symmetric Does not suffer from any insertion anomaly. Free from update anomalies. Free from delete anomalies One to One, One to many, Many to many relationships Based on relational data structures Relational databases are what brings many sources into a common query (such as SQL) Retrieve algorithms are simple and symmetric Does not suffer from any insert anomaly. Free form update anomalies Free from delete anomalies The Entity-Relationship (ER) Model: An E-R model is a particular type of data model suited to designing relational databases. ER- Model is a visual representation of data that describes how data entities being modeled and the relationships between these data entities. Fig ER- Model

7 Module 2 : Entity-Relationship Model 21 E-R Symbols and Notations: Fig ER Symbols and Notations Components of E-R Diagram The E-R Model has three main components. 1) Entity: An Entity can be any object, place, person or class. In E-R Diagram, an entity is represented using rectangles. Consider an example of an Organization. Employee, Manager, Department, Product and many more can be taken as entities from an Organization. Fig ER Model

8 Database Management System Types of Entity: Attribute Type Description Example Strong Entity Types Strong Entity are the entities which has a key attribute in its attribute list or a set that has a primary key. The strong entity type is also called regular entity type. The Employee s SSN is a unique. So, SSN is set to be the Primary Key of the STUDENT entity, & Hence Employee is a strong entity type because of its key attribute. Weak Entity Types Entity Type with no key or Primary Key are called weak entity Type. CHILD is a WEAK entity type and Employee is the OWNER entity type. Fig Strong & Weak Entity Types in ER Model 2) Attribute: An Attribute describes a property or characteristic of an entity. For example, Name, Age, Address etc can be attributes of a Student. An attribute is represented using eclipse. 2.1 Types of Attributes: Attribute Type Simple attribute Single-value attribute Multi-value attribute Key Attribute Description Simple attributes are atomic values, which cannot be divided further. Single-value attribute contain single value. Multi-value attribute may contain more than one values Key attribute represents the main characteristic of an Entity. It is used to represent Primary key Example A Student s phone number is an atomic value of 10 digits. A Student have only one roll number A student can have more than one phone number, _address, etc A Student s roll number Composite attribute Composite attribute are made of more than one simple attribute. A student's address may have door number street name,city and pin code.

9 Module 2 : Entity-Relationship Model 23 Derived attributes Derived attributes are the attributes that do not exist in the physical database, but their values are derived from other attributes present in the database. Age of the student can be derived from data_of_birth Fig Types of Attributes in ER Model 3) Relationship: A Relationship describes relations between entities. Relationship is represented using diamonds. Fig Relationship in ER Model The degree of a relationship is the number of entity types that participate in the relationship. There are three types of relationship that exist between Entities. 1. Binary Relationship 2. Unary Relationship 3. Ternary Relationship 1. Binary Relationship: Binary Relationship means relation between two Entities. This is further divided into three types. 1.1 One to One: This type of relationship is rarely seen in real world. Fig One to One Binary Relationship

10 Database Management System 24 The above example describes that one student can enroll only for one course and a course will also have only one Student. This is not what you will usually see in relationship. 1.2 One to Many: It reflects business rule that one entity is associated with many number of same entity. The example for this relation might sound a little weird, but this means that one student can enroll to many courses, but one course will have one Student. Fig One to Many Binary Relationship 1.3 Many to One: It reflects business rule that many entities can be associated with just one entity. For example, Student enrolls for only one Course but a Course can have many Students. 1.4 Many to Many: Fig Many to One Binary Relationship Fig Many to Many Binary Relationship The above diagram represents that many students can enroll for more than one courses. 2. Unary Relationship: A unary relationship is when both participants in the relationship are the same entity. Fig Unary Relationship

11 Module 2 : Entity-Relationship Model 25 The above diagram represents that one customer is marred with another customer 3 Ternary Relationship: Relationship of degree three is called Ternary relationship. Fig Ternary Relationship In the above diagram, Customer purchase item from RetailOutlet. Participation Constraints A participation constraint defines the number of times an entity can participate in a connected relationship. There are two types of Participation constraints 1. Total Participation each entity is involved in the relationship. Total participation is represented by double lines. 2. Partial participation Not all entities are involved in the relationship. Partial participation is represented by single lines. Fig Participation Constraints Generalization: The ER Model has the power of expressing database entities in a conceptual hierarchical manner. As the hierarchy goes up, it generalizes the view of entities, and as we go deep in the hierarchy, it gives us the detail of every entity included. Generalization is the process of defining general entity types from a set of specialized entity types by identifying their common characteristics. In other words, this process minimizes the differences between entities by identifying a general entity type that features the common attributes of specialized entities. Generalization is a bottom-up approach as it starts with the specialized entity types (subclasses) and forms a generalized entity type (superclass).

12 Database Management System 26 Fig STAFF, FACULTY, and STUDENT entities before generalization For example, suppose that someone has given us the specialized entity types FACULTY, STAFF, and STUDENT, and we want to represent these entity types separately in the E-R model as depicted in above Fig However, if we examine them closely, we can observe that a number of attributes are common to all entity types, while others are specific to a particular entity. For example, FACULTY, STAFF, and STUDENT all share the attributes Name, SSN, Birth Date, Address, and . On the other hand, attributes such as GPA, Class, and Major Dept are specific to the STUDENTS; OfficePhone is specific to FACULTY, and Designation is specific to STAFF. Common attributes suggest that each of these three entity types is a form of a more general entity type. This general entity type is simply a PERSON superclass entity with common attributes of three subclasses (see Figure 2.19)Thus, in the generalization process, we group specialized entity types to form one general entity type and identify common attributes of specialized entities as attributes of a general entity type. The general entity type is a superclass of specialized entity types or subclasses. Fig PERSON superclass and FACULTY,STAFF, and STUDENT subclasses after generalization.

13 Module 2 : Entity-Relationship Model 27 Generalization is a bottom-up approach in which two lower level entities combine to form a higher level entity. In generalization, the higher level entity can also combine with other lower level entity to make further higher level entity Specialization: Specialization is the process of defining one or more subclasses of a superclass by identifying its distinguishing characteristics. Unlike generalization, specialization is thus a top-down approach. It starts with the general entity (superclass) and forms specialized entity types (subclasses) based on specialized attributes or relationships specific to a subclass. Fig LIBRARY ITEM entity before specialization For example, consider Figure 2.20 LIBRARY ITEM is an entity type with several attributes such as IdentificationNo, RecordingDate, Frequency, and Edition. After careful review of these items, it should become clear that some items such as books do not have values for attributes such as Frequency, RecordingDate, and CourseNo, while Video CDs do not have an Author or an Edition. In addition, all items have common attributes such as IdentificationNo, Location, and Subject. Someone creating a library database, then, could use the specialization process to identify superclass and subclass relationships. In this case, the original entity LIBRARY ITEM forms a superclass entity type made up of attributes shared by all items, while specialized items with distinguishing attributes, such as BOOK, JOURNALS, and VIDEOCD, form subclasses. Fig LIBRARY ITEM superclass and BOOK, JOURNAL, and VIDEOCD subclasses after specialization.

14 Database Management System Aggregation: The E-R model cannot express relationships among relationships. Consider a DB with information about employees who work on a particular project and use a number of machines doing that work. We get the E-R diagram shown in Fig Fig E-R diagram with redundant relationships Relationship sets work and uses could be combined into a single set. However, they shouldn't be, as this would obscure the logical structure of this scheme. The solution is to use aggregation. An abstraction through which relationships are treated as higher-level entities. For our example, we treat the relationship set work and the entity sets employee and project as a higher-level entity set called work. Figure 2.22 shows the E-R diagram with aggregation. Fig E-R diagram with aggregation

15 Module 2 : Entity-Relationship Model Step by Step Approach for making a Entity Relationship (ER) Model: Example we want to design an Entity Relationship (ER) model for a college database. Say we have the following statements. A college contains many departments Each department can offer any number of courses Many instructors can work in a department An instructor can work only in one department For each department there is a Head An instructor can be head of only one department Each instructor can take any number of courses A course can be taken by only one instructor A student can enroll for any number of courses Each course can have any number of students Step 1 : Identify the Entities What are the entities here? From the statements given, the entities are Department Course Instructor Student Stem 2 : Identify the relationships One department offers many courses. But one particular course can be offered by only one department. hence the cardinality between department and course is One to Many (1:N) One department has multiple instructors. But instructor belongs to only one department. Hence the cardinality between department and instructor is One to Many (1:N) One department has only one head and one head can be the head of only one department. Hence the cardinality is one to one. (1:1) One course can be enrolled by many students and one student can enroll for many courses. Hence the cardinality between course and student is Many to Many (M:N) One course is taught by only one instructor. But one instructor teaches many courses. Hence the cardinality between course and instructor is Many to One (N :1) Step 3: Identify the key attributes "Departmen_Name" can identify a department uniquely. Hence Department_Name is the key attribute for the Entity "Department". Course_ID is the key attribute for "Course" Entity. Student_ID is the key attribute for "Student" Entity. Instructor_ID is the key attribute for "Instructor" Entity. Step 4: Identify other relevant attributes For the department entity, other attributes are location For course entity, other attributes are course_name,duration For instructor entity, other attributes are first_name, last_name, phone For student entity, first_name, last_name, phone

16 Database Management System 30 Step 5: Draw complete ER diagram By connecting all these details, we can now draw ER diagram as given below. Fig E-R Model for College Database Advantages of ER Modeling: 1. ER Modeling is simple and easily understandable. It is represented in business users language and it can be understood by non-technical specialist. 2. Intuitive and helps in Physical Database creation. 3. Can be generalized and specialized based on needs. 4. Can help in database design. 5. Gives a higher level description of the system.

17 Module 2 : Entity-Relationship Model 31 Disadvantages of ER Modeling: 1. Physical design derived from E-R Model may have some amount of ambiguities or inconsistency. 2. Sometime diagrams may lead to misinterpretations Extended Entity-Relationship (EER) Model: We have illustrated the basic concepts of the entity-relationship model. These concepts are generally adequate to design solutions for common business problems. However, since the early 1980s, business database applications and database requirements have changed dramatically. Business relationships and business data have become much more complex as applications such as multimedia systems, geographical information systems, and computer-aided engineering have gained prominence. These applications demand more complex database requirements than traditional applications, rendering the basic concepts of E-R modeling inadequate. As a result, researchers in the 80s enhanced the original E-R model to form the enhanced entity relationship (EE-R) model Features of EER Model: EER creates a design more accurate to database schemas. It reflects the data properties and constraints more precisely. It includes all modeling concepts of the ER model. Diagrammatic technique helps for displaying the EER schema. It includes the concept of specialization and generalization. It is used to represent a collection of objects that is union of objects of different of different entity types Sub Class and Super Class: Sub class and Super class relationship leads the concept of Inheritance. The relationship between sub class and super class is denoted with symbol. 1. Super Class: Super class is an entity type that has a relationship with one or more subtypes.an entity cannot exist in database merely by being member of any super class. For example: Shape super class is having sub groups as Square, Circle, Triangle. 2. Sub Class Sub class is a group of entities with unique attributes. Sub class inherits properties and attributes from its super class. For example: Square, Circle, Triangle are the sub class of Shape super class.

18 Database Management System Objective Type Questions: Fig Super Class/Sub Class Relationship 1) An is a set of entities of the same type that share the same properties, or attributes. a) Entity set b) Attribute set c) Relation set d) Entity model 2) The descriptive property possessed by each entity set is. a) Entity b) Attribute c) Relation d) Model 3) The function that an entity plays in a relationship is called that entity s. a) Participation b) Position c) Role d) Instance 4) Which of the following is a single valued attribute a) Register_number b) Address c) SUBJECT_TAKEN d) Reference 5) In a relation between the entities the type and condition of the relation should be specified. That is called as attribute a) Desciptive b) Derived c) Recursive d) Relative 6) The entity relationship set is represented in E-R diagram as a) Double diamonds b) Undivided rectangles c) Dashed lines d) Diamond 7) For a weak entity set to be meaningful, it must be associated with another entity set, called the a) Identifying set

19 Module 2 : Entity-Relationship Model 33 b) Owner set c) Neighbour set d) Strong entity set 8) Let us consider phone_number,which can take single or several values. Treatingphone_numberas an permits instructors to have several phone numbers (including zero) associated with them. a) Entity b) Attribute c) Relation d) Value 9) The total participation by entities is represented in E-R diagram as a) Dashed line b) Double line c) Double rectangle d) Circle 10) Which of the following indicates the maximum number of entities that can be involved in a relationship? a) Minimum cardinality b) Maximum cardinality c) ERD d) Greater Entity Count 11) What is a relationship called when it is maintained between two entities? a) Unary b) Binary c) Ternary d) Quaternary 12) A primary key is combined with a foreign key creates a) Parent-Child relation ship between the tables that connect them b) Many to many relationship between the tables that connect them c) Network model between the tables that connect them d) None of the mentioned 13) The entity set person is classified as student and employee.this process is called a) Generalization b) Specialization c) Inheritance d) Constraint generalization 14) The refinement from an initial entity set into successive levels of entity subgroupings represents a design process in which distinctions are made explicit. a) Hierarchy b) Bottom-up c) Top-down d) Radical 15) If an entity set is a lower-level entity set in more than one ISA relationship, then the entity set has a) Hierarchy b) Multilevel inheritance c) Single inheritance d) Multiple inheritance

20 Database Management System 34 16) A constraint requires that an entity belong to no more than one lower-level entity set. a) Disjointness b) Uniqueness c) Special d) Relational 17) The completeness constraint may be one of the following: Total generalization or specialization, Partial generalization or specialization. Which is the default? a) Total b) Partial c) Should be specified d) Cannot be determined 18) Which of the following is another name for weak entity? a) Child b) Owner c) Dominant d) All of the mentioned Answers :- Question Ans. a b c a a d a a b b Question Ans. b a b c d a b a 2.8. Short Answer Questions: 1) Define Entity, Entity Set, and extensions of entity set. Give one example for each? 2) Define and give examples to illustrate the four types of attributes in database? 3) Define relationship and participation? 4) Define mapping cardinality or cardinality ratio? 5) Explain the four types of mapping cardinality with example? 6) Define weak Entity set. Give an example and explain why it is weak entity set? 7) Define discriminator or partial key of a weak entity set. Give example? 2.9 Long Answer Questions: 1) Explain about various data models 2) Give example of following relationships : (i) Many-to-One (ii) One-to-One (iii) One-to-Many (iv) Many-to-Many 3) Discuss with examples about various types of attributes present in the ER model. 4) What are the different types of attributes? Explain with example

21 Module 2 : Entity-Relationship Model Case Study: Case Study on ER Diagram: 1) Suppose you are given the following requirements for a simple database for the National Hockey League (NHL): the NHL has many teams, each team has a name, a city, a coach, a captain, and a set of players, each player belongs to only one team, each player has a name, a position (such as left wing or goalie), a skill level, and a set of injury records, a team captain is also a player, a game is played between two teams (referred to as host_team and guest_team) and has a date (such as May 11th, 1999) and a score (such as 4 to 2).Construct a clean and concise ER diagram for the NHL database. 2) A university registrar s office maintains data about the following entities: 1. courses, including number, title, credits, syllabus, and prerequisites; 2. course offerings, including course number, year, semester, section number, instructor(s), timings, and classroom; 3. students, including student-id, name, and program; 4. Instructors, including identification number, name, department, and title. Further, the enrollment of students in courses and grades awarded to students in each course they are enrolled for must be appropriately modeled. Construct an E-R diagram for the registrar s office. Document all assumptions that you make about the mapping constraints. 3) Construct an E-R diagram for a hospital with a set of patients and a set of medical doctors. Associate with each patient a log of the various tests and examinations conducted. 4) Design an E-R diagram for keeping track of the exploits of your favorite sports team. You should store the matches played, the scores in each match, the players in each match and individual player statistics for each match. Summary statistics should be modeled as derived attributes. 5) Construct an E-R diagram for a car-insurance company whose customers own one or more cars each. Each car has associated with it zero to any number of recorded accidents

22 Database Management System 36 6) Construct an E-R diagram for a hospital with a set of patients and a set of medical doctors. Associate with each patient a log of the various tests and examinations conducted. 7) Design an E-R diagram for keeping track of the exploits of your favourite sports team. You should store the matches played, the scores in each match, the players in each match and individual player statistics for each match. Summary statistics should be modeled as derived attributes.

23 Module 2 : Entity-Relationship Model References: 1. G. K. Gupta : Database Management Systems, McGraw Hill. 2. Korth, Slberchatz,Sudarshan, : Database System Concepts, 6th Edition, McGraw Hill 3. Elmasri and Navathe, Fundamentals of Database Systems, 5thEdition, PEARSON Education. Practice for Module 2 1) Draw an ER diagram for a database that keeps track of company and employee phones. Assume that an employee may work in up to 2 departments but may also not be assigned to any department. Employee may or may not have personal phone but a department must have one and have up to three phone numbers including employees personal phone number. (10 M) 2) Consider the ER diagram given below. Assume that a subject may or may not use a textbook, but that a text by definition is a book that is used in some subject. A subject may not use more than 5 books. Instructors teach from 2 to 4 subjects. (10 M) 3) The Accounting department in a company keeps the information about its employees in a database.the employees are classified as part-time employees, full-time employees, and interns. Interns are usually students who work with the company during the summers. Complete the EE-R diagram below by: a. Adding a unique attribute (relationship) for each entity subtype b. Adding an attribute shared by all entities c. Identifying whether the disjoint or overlap rule applies d. Identifying whether the total specialization or partial specialization rule applies (10 M) Self-assessment

24 Database Management System 38 1) A university registrar s office maintains data about the following entities: Courses, including number, title, credits, syllabus, and prerequisites; Course offerings, including course number, year, semester, section number, instructor(s), timings, and classroom; Students, including student-id, name, and program; Instructors, including identification number, name, department, and title. Further, the enrollment of students in courses and grades awarded to students in each course they are enrolled for must be appropriately modeled. Construct a E-R diagram for registrar s office. Document all assumptions that you make about the mapping constraints 2) Explain the significance of ER Model for Database design? 3) Enumerate the basic constructs of ER Model

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