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Chapter 3 Data Modeling Using the Entity-Relationship (ER) Model Copyright © 2004 Pearson Education, Inc.
Chapter Outline Example Database Application (COMPANY) ER Model Concepts Entities and Attributes Entity Types, Value Sets, and Key Attributes Relationships and Relationship Types Weak Entity Types Roles and Attributes in Relationship Types ER Diagrams - Notation ER Diagram for COMPANY Schema Alternative Notations – UML class diagrams, others
Example COMPANY Database Requirements of the Company (oversimplified for illustrative purposes) The company is organized into DEPARTMENTs. Each department has a name, number and an employee who  manages  the department. We keep track of the start date of the department   manager.   Each department  controls  a number of PROJECTs .  Each project has a name, number and is   located at a single location.
Example COMPANY Database (Cont.) We store each EMPLOYEE’s social security number, address, salary, sex, and birthdate. Each employee  works for  one department but may  work on  several projects. We keep track of the number of hours per week that an employee currently works on each project. We also keep track of the  direct supervisor  of each employee. Each employee may  have  a number of DEPENDENTs. For each dependent, we keep track of their name, sex, birthdate, and relationship to employee.
ER Model Concepts Entities and Attributes Entities are specific objects or things in the mini-world that are represented in the database. For example the EMPLOYEE John Smith, the Research DEPARTMENT, the ProductX PROJECT Attributes are properties used to describe an entity. For example an EMPLOYEE entity may have a Name, SSN, Address, Sex, BirthDate A specific entity will have a value for each of its attributes. For example a specific employee entity may have Name='John Smith', SSN='123456789', Address ='731, Fondren, Houston, TX', Sex='M', BirthDate='09-JAN-55‘ Each attribute has a  value set  (or data type) associated with it – e.g. integer, string, subrange, enumerated type, …
Types of Attributes (1) Simple Each entity has a single atomic value for the attribute. For example, SSN or Sex. Composite The attribute may be composed of several components. For example, Address (Apt#, House#, Street, City, State, ZipCode, Country) or Name (FirstName, MiddleName, LastName). Composition may form a hierarchy where some components are themselves composite. Multi-valued An entity may have multiple values for that attribute. For example, Color of a CAR or PreviousDegrees of a STUDENT. Denoted as {Color} or {PreviousDegrees}.
Types of Attributes (2) In general, composite and multi-valued attributes may be nested arbitrarily to any number of levels although this is rare. For example, PreviousDegrees of a STUDENT is a composite multi-valued attribute denoted by {PreviousDegrees (College, Year, Degree, Field)}.
Entity Types and Key Attributes Entities with the same basic attributes are grouped or typed into an entity type. For example, the EMPLOYEE entity type or the PROJECT entity type. An attribute of an entity type for which each entity must have a unique value is called a key attribute of the entity type. For example, SSN of EMPLOYEE. A key attribute may be composite. For example, VehicleTagNumber is a key of the CAR entity type with components (Number, State). An entity type may have more than one key. For example, the CAR entity type may have two keys: VehicleIdentificationNumber (popularly called VIN) and VehicleTagNumber (Number, State), also known as license_plate number.
ENTITY SET corresponding to the ENTITY TYPE CAR car 1 ((ABC 123, TEXAS), TK629, Ford Mustang, convertible, 1999, {red, black}) car 2 ((ABC 123, NEW YORK), WP9872, Nissan 300ZX, 2-door, 2002, {blue}) car 3 ((VSY 720, TEXAS), TD729, Buick LeSabre, 4-door, 2003, {white, blue}) . . . CAR Registration(RegistrationNumber, State), VehicleID, Make, Model, Year, {Color}
SUMMARY OF ER-DIAGRAM  NOTATION FOR ER SCHEMAS Meaning ENTITY TYPE WEAK ENTITY TYPE RELATIONSHIP TYPE IDENTIFYING RELATIONSHIP TYPE ATTRIBUTE KEY ATTRIBUTE MULTIVALUED ATTRIBUTE COMPOSITE ATTRIBUTE DERIVED ATTRIBUTE TOTAL PARTICIPATION OF E 2  IN R CARDINALITY RATIO 1:N FOR E 1 :E 2  IN R STRUCTURAL CONSTRAINT (min, max) ON PARTICIPATION OF E IN R Symbol R E 2 E 1 R E 2 R (min,max) E N E 1
ER DIAGRAM – Entity Types are: EMPLOYEE, DEPARTMENT, PROJECT, DEPENDENT
Relationships and Relationship Types (1) A relationship relates two or more distinct entities with a specific meaning. For example, EMPLOYEE John Smith works on the ProductX PROJECT or EMPLOYEE Franklin Wong manages the Research DEPARTMENT. Relationships of the same type are grouped or typed into a relationship type. For example, the WORKS_ON relationship type in which EMPLOYEEs and PROJECTs participate, or the MANAGES relationship type in which EMPLOYEEs and DEPARTMENTs participate. The degree of a relationship type is the number of participating entity types. Both MANAGES and WORKS_ON are binary relationships.
Example relationship instances of the WORKS_FOR relationship between EMPLOYEE and DEPARTMENT e 1   e 2   e 3   e 4   e 5   e 6   e 7   EMPLOYEE r 1 r 2 r 3 r 4 r 5 r 6 r 7 WORKS_FOR    d 1    d 2    d 3 DEPARTMENT
Example relationship instances of the WORKS_ON relationship between EMPLOYEE and PROJECT e 1   e 2   e 3   e 4   e 5   e 6   e 7   r 1 r 2 r 3 r 4 r 5 r 6 r 7    p 1    p 2    p 3 r 8 r 9
Relationships and Relationship Types (2) More than one relationship type can exist with the same participating entity types. For example, MANAGES and WORKS_FOR are distinct relationships between EMPLOYEE and DEPARTMENT, but with different meanings and different relationship instances.
ER DIAGRAM – Relationship Types are: WORKS_FOR, MANAGES, WORKS_ON, CONTROLS, SUPERVISION, DEPENDENTS_OF
Weak Entity Types An entity that does not have a key attribute A weak entity must participate in an identifying relationship type with an owner or identifying entity type Entities are identified by the combination of: A partial key of the weak entity type The particular entity they are related to in the identifying entity type Example:   Suppose that a DEPENDENT entity is identified by the dependent’s first name and birhtdate,  and  the specific EMPLOYEE that the dependent is related to.  DEPENDENT is a weak entity type with EMPLOYEE as its identifying entity type via the identifying relationship type DEPENDENT_OF
Weak Entity Type is:  DEPENDENT Identifying Relationship is:  DEPENDENTS_OF
Constraints on Relationships Constraints on Relationship Types ( Also known as ratio constraints ) Maximum Cardinality One-to-one (1:1) One-to-many (1:N) or Many-to-one (N:1) Many-to-many Minimum Cardinality (also called participation constraint or existence dependency constraints) zero (optional participation, not existence-dependent) one or more (mandatory, existence-dependent)
Many-to-one (N:1) RELATIONSHIP e 1   e 2   e 3   e 4   e 5   e 6   e 7   EMPLOYEE r 1 r 2 r 3 r 4 r 5 r 6 r 7 WORKS_FOR    d 1    d 2    d 3 DEPARTMENT
Many-to-many (M:N) RELATIONSHIP e 1   e 2   e 3   e 4   e 5   e 6   e 7   r 1 r 2 r 3 r 4 r 5 r 6 r 7    p 1    p 2    p 3 r 8 r 9
Relationships and Relationship Types (3) We can also have a  recursive  relationship type. Both participations are same entity type in different roles. For example, SUPERVISION relationships between EMPLOYEE (in role of supervisor or boss) and (another) EMPLOYEE (in role of subordinate or worker). In following figure, first role participation labeled with 1 and second role participation labeled with 2. In ER diagram, need to display role names to distinguish participations.
A RECURSIVE RELATIONSHIP  SUPERVISION e 1   e 2   e 3   e 4   e 5   e 6   e 7   EMPLOYEE r 1 r 2 r 3 r 4 r 5 r 6 SUPERVISION 2 1 1 2 2 1 1 1 2 1 2 2 © The Benjamin/Cummings Publishing Company, Inc. 1994, Elmasri/Navathe, Fundamentals of Database Systems, Second Edition
Recursive Relationship Type is:  SUPERVISION (participation role names are shown)
Attributes of Relationship types A relationship type can have attributes; for example, HoursPerWeek of WORKS_ON; its value for each relationship instance describes the number of hours per week that an EMPLOYEE works on a PROJECT.
Attribute of a Relationship Type is:  Hours of WORKS_ON
Structural Constraints –  one way to express semantics  of relationships Structural constraints on relationships: Cardinality ratio  (of a binary relationship): 1:1, 1:N, N:1, or M:N SHOWN BY PLACING APPROPRIATE NUMBER ON THE LINK. Participation constraint  (on each participating entity type): total (called  existence dependency ) or partial. SHOWN BY DOUBLE LINING THE LINK NOTE: These are easy to specify  for Binary Relationship   Types .
Alternative (min, max) notation for relationship structural constraints: Specified on  each participation  of an entity type E in a relationship type R Specifies that each entity e in E participates in  at least  min and  at most  max relationship instances in R Default(no constraint): min=0, max=n Must have min  max, min  0, max   1 Derived from the knowledge of mini-world constraints Examples: A department has  exactly one  manager and an employee can manage  at most one  department. Specify (0,1) for participation of EMPLOYEE in MANAGES Specify (1,1) for participation of DEPARTMENT in MANAGES An employee can work for  exactly one  department but a department can have  any number of employees . Specify (1,1) for participation of EMPLOYEE in WORKS_FOR Specify (0,n) for participation of DEPARTMENT in WORKS_FOR
The (min,max) notation relationship constraints Employee Department Manages (1,1) (0,1) Employee Department Works-for (1,N) (1,1)
COMPANY ER Schema Diagram  using (min, max) notation
Relationships of Higher Degree Relationship types of degree 2 are called  binary Relationship types of degree 3 are called  ternary  and of degree n are called  n-ary In general, an n-ary relationship  is not  equivalent to n binary relationships Higher-order relationships discussed further in Chapter 4
Data Modeling Tools A number of popular tools that cover conceptual modeling and mapping into relational schema design. Examples: ERWin, S- Designer (Enterprise Application Suite), ER- Studio,  etc. POSITIVES: serves as documentation of application requirements, easy user interface - mostly graphics editor support
Problems with Current Modeling Tools DIAGRAMMING Poor conceptual meaningful notation. To avoid the problem of layout algorithms and aesthetics of diagrams, they prefer boxes and lines and do nothing more than represent (primary-foreign key) relationships among resulting tables.(a few exceptions) METHODOLGY lack of built-in methodology support. poor tradeoff analysis or user-driven design preferences. poor design verification and suggestions for improvement.
Some of the Currently Available Automated Database  Design Tools Data modeling, design and reengineering Visual Basic and Visual C++ Visio Enterprise Visio Data modeling, business logic modeling Enterprise Application Suite Sybase Conceptual modeling up to code maintenance Xcase Resolution Ltd. Mapping from O-O to relational model RW Metro Rogue Ware Modeling in UML and application generation in C++ and JAVA Rational Rose Rational Mapping from O-O to relational model Pwertier Persistence Inc. Data, process, and business component modeling Platinum Enterprice Modeling Suite: Erwin, BPWin, Paradigm Plus Platinum Technology Data modeling, object modeling, process modeling, structured analysis/design System Architect 2001 Popkin Software Database modeling, application development Developer 2000 and Designer 2000 Oracle Database administration and space and security management DB Artisan Database Modeling in ER and IDEF1X ER Studio Embarcadero Technologies FUNCTIONALITY TOOL COMPANY
ER DIAGRAM FOR A BANK  DATABASE © The Benjamin/Cummings Publishing Company, Inc. 1994, Elmasri/Navathe, Fundamentals of Database Systems, Second Edition
PROBLEM with ER notation THE ENTITY RELATIONSHIP MODEL IN ITS ORIGINAL FORM DID NOT  SUPPORT THE SPECIALIZATION/ GENERALIZATION ABSTRACTIONS
Extended Entity-Relationship (EER) Model Incorporates Set-subset relationships Incorporates Specialization/Generalization Hierarchies NEXT CHAPTER ILLUSTRATES HOW THE ER MODEL CAN BE EXTENDED WITH  -  Set-subset relationships and Specialization/Generalization Hierarchies and how to display them in EER diagrams

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03 Ch3 Notes Revised

  • 1.  
  • 2. Chapter 3 Data Modeling Using the Entity-Relationship (ER) Model Copyright © 2004 Pearson Education, Inc.
  • 3. Chapter Outline Example Database Application (COMPANY) ER Model Concepts Entities and Attributes Entity Types, Value Sets, and Key Attributes Relationships and Relationship Types Weak Entity Types Roles and Attributes in Relationship Types ER Diagrams - Notation ER Diagram for COMPANY Schema Alternative Notations – UML class diagrams, others
  • 4. Example COMPANY Database Requirements of the Company (oversimplified for illustrative purposes) The company is organized into DEPARTMENTs. Each department has a name, number and an employee who manages the department. We keep track of the start date of the department manager. Each department controls a number of PROJECTs . Each project has a name, number and is located at a single location.
  • 5. Example COMPANY Database (Cont.) We store each EMPLOYEE’s social security number, address, salary, sex, and birthdate. Each employee works for one department but may work on several projects. We keep track of the number of hours per week that an employee currently works on each project. We also keep track of the direct supervisor of each employee. Each employee may have a number of DEPENDENTs. For each dependent, we keep track of their name, sex, birthdate, and relationship to employee.
  • 6. ER Model Concepts Entities and Attributes Entities are specific objects or things in the mini-world that are represented in the database. For example the EMPLOYEE John Smith, the Research DEPARTMENT, the ProductX PROJECT Attributes are properties used to describe an entity. For example an EMPLOYEE entity may have a Name, SSN, Address, Sex, BirthDate A specific entity will have a value for each of its attributes. For example a specific employee entity may have Name='John Smith', SSN='123456789', Address ='731, Fondren, Houston, TX', Sex='M', BirthDate='09-JAN-55‘ Each attribute has a value set (or data type) associated with it – e.g. integer, string, subrange, enumerated type, …
  • 7. Types of Attributes (1) Simple Each entity has a single atomic value for the attribute. For example, SSN or Sex. Composite The attribute may be composed of several components. For example, Address (Apt#, House#, Street, City, State, ZipCode, Country) or Name (FirstName, MiddleName, LastName). Composition may form a hierarchy where some components are themselves composite. Multi-valued An entity may have multiple values for that attribute. For example, Color of a CAR or PreviousDegrees of a STUDENT. Denoted as {Color} or {PreviousDegrees}.
  • 8. Types of Attributes (2) In general, composite and multi-valued attributes may be nested arbitrarily to any number of levels although this is rare. For example, PreviousDegrees of a STUDENT is a composite multi-valued attribute denoted by {PreviousDegrees (College, Year, Degree, Field)}.
  • 9. Entity Types and Key Attributes Entities with the same basic attributes are grouped or typed into an entity type. For example, the EMPLOYEE entity type or the PROJECT entity type. An attribute of an entity type for which each entity must have a unique value is called a key attribute of the entity type. For example, SSN of EMPLOYEE. A key attribute may be composite. For example, VehicleTagNumber is a key of the CAR entity type with components (Number, State). An entity type may have more than one key. For example, the CAR entity type may have two keys: VehicleIdentificationNumber (popularly called VIN) and VehicleTagNumber (Number, State), also known as license_plate number.
  • 10. ENTITY SET corresponding to the ENTITY TYPE CAR car 1 ((ABC 123, TEXAS), TK629, Ford Mustang, convertible, 1999, {red, black}) car 2 ((ABC 123, NEW YORK), WP9872, Nissan 300ZX, 2-door, 2002, {blue}) car 3 ((VSY 720, TEXAS), TD729, Buick LeSabre, 4-door, 2003, {white, blue}) . . . CAR Registration(RegistrationNumber, State), VehicleID, Make, Model, Year, {Color}
  • 11. SUMMARY OF ER-DIAGRAM NOTATION FOR ER SCHEMAS Meaning ENTITY TYPE WEAK ENTITY TYPE RELATIONSHIP TYPE IDENTIFYING RELATIONSHIP TYPE ATTRIBUTE KEY ATTRIBUTE MULTIVALUED ATTRIBUTE COMPOSITE ATTRIBUTE DERIVED ATTRIBUTE TOTAL PARTICIPATION OF E 2 IN R CARDINALITY RATIO 1:N FOR E 1 :E 2 IN R STRUCTURAL CONSTRAINT (min, max) ON PARTICIPATION OF E IN R Symbol R E 2 E 1 R E 2 R (min,max) E N E 1
  • 12. ER DIAGRAM – Entity Types are: EMPLOYEE, DEPARTMENT, PROJECT, DEPENDENT
  • 13. Relationships and Relationship Types (1) A relationship relates two or more distinct entities with a specific meaning. For example, EMPLOYEE John Smith works on the ProductX PROJECT or EMPLOYEE Franklin Wong manages the Research DEPARTMENT. Relationships of the same type are grouped or typed into a relationship type. For example, the WORKS_ON relationship type in which EMPLOYEEs and PROJECTs participate, or the MANAGES relationship type in which EMPLOYEEs and DEPARTMENTs participate. The degree of a relationship type is the number of participating entity types. Both MANAGES and WORKS_ON are binary relationships.
  • 14. Example relationship instances of the WORKS_FOR relationship between EMPLOYEE and DEPARTMENT e 1  e 2  e 3  e 4  e 5  e 6  e 7  EMPLOYEE r 1 r 2 r 3 r 4 r 5 r 6 r 7 WORKS_FOR  d 1  d 2  d 3 DEPARTMENT
  • 15. Example relationship instances of the WORKS_ON relationship between EMPLOYEE and PROJECT e 1  e 2  e 3  e 4  e 5  e 6  e 7  r 1 r 2 r 3 r 4 r 5 r 6 r 7  p 1  p 2  p 3 r 8 r 9
  • 16. Relationships and Relationship Types (2) More than one relationship type can exist with the same participating entity types. For example, MANAGES and WORKS_FOR are distinct relationships between EMPLOYEE and DEPARTMENT, but with different meanings and different relationship instances.
  • 17. ER DIAGRAM – Relationship Types are: WORKS_FOR, MANAGES, WORKS_ON, CONTROLS, SUPERVISION, DEPENDENTS_OF
  • 18. Weak Entity Types An entity that does not have a key attribute A weak entity must participate in an identifying relationship type with an owner or identifying entity type Entities are identified by the combination of: A partial key of the weak entity type The particular entity they are related to in the identifying entity type Example: Suppose that a DEPENDENT entity is identified by the dependent’s first name and birhtdate, and the specific EMPLOYEE that the dependent is related to. DEPENDENT is a weak entity type with EMPLOYEE as its identifying entity type via the identifying relationship type DEPENDENT_OF
  • 19. Weak Entity Type is: DEPENDENT Identifying Relationship is: DEPENDENTS_OF
  • 20. Constraints on Relationships Constraints on Relationship Types ( Also known as ratio constraints ) Maximum Cardinality One-to-one (1:1) One-to-many (1:N) or Many-to-one (N:1) Many-to-many Minimum Cardinality (also called participation constraint or existence dependency constraints) zero (optional participation, not existence-dependent) one or more (mandatory, existence-dependent)
  • 21. Many-to-one (N:1) RELATIONSHIP e 1  e 2  e 3  e 4  e 5  e 6  e 7  EMPLOYEE r 1 r 2 r 3 r 4 r 5 r 6 r 7 WORKS_FOR  d 1  d 2  d 3 DEPARTMENT
  • 22. Many-to-many (M:N) RELATIONSHIP e 1  e 2  e 3  e 4  e 5  e 6  e 7  r 1 r 2 r 3 r 4 r 5 r 6 r 7  p 1  p 2  p 3 r 8 r 9
  • 23. Relationships and Relationship Types (3) We can also have a recursive relationship type. Both participations are same entity type in different roles. For example, SUPERVISION relationships between EMPLOYEE (in role of supervisor or boss) and (another) EMPLOYEE (in role of subordinate or worker). In following figure, first role participation labeled with 1 and second role participation labeled with 2. In ER diagram, need to display role names to distinguish participations.
  • 24. A RECURSIVE RELATIONSHIP SUPERVISION e 1  e 2  e 3  e 4  e 5  e 6  e 7  EMPLOYEE r 1 r 2 r 3 r 4 r 5 r 6 SUPERVISION 2 1 1 2 2 1 1 1 2 1 2 2 © The Benjamin/Cummings Publishing Company, Inc. 1994, Elmasri/Navathe, Fundamentals of Database Systems, Second Edition
  • 25. Recursive Relationship Type is: SUPERVISION (participation role names are shown)
  • 26. Attributes of Relationship types A relationship type can have attributes; for example, HoursPerWeek of WORKS_ON; its value for each relationship instance describes the number of hours per week that an EMPLOYEE works on a PROJECT.
  • 27. Attribute of a Relationship Type is: Hours of WORKS_ON
  • 28. Structural Constraints – one way to express semantics of relationships Structural constraints on relationships: Cardinality ratio (of a binary relationship): 1:1, 1:N, N:1, or M:N SHOWN BY PLACING APPROPRIATE NUMBER ON THE LINK. Participation constraint (on each participating entity type): total (called existence dependency ) or partial. SHOWN BY DOUBLE LINING THE LINK NOTE: These are easy to specify for Binary Relationship Types .
  • 29. Alternative (min, max) notation for relationship structural constraints: Specified on each participation of an entity type E in a relationship type R Specifies that each entity e in E participates in at least min and at most max relationship instances in R Default(no constraint): min=0, max=n Must have min  max, min  0, max  1 Derived from the knowledge of mini-world constraints Examples: A department has exactly one manager and an employee can manage at most one department. Specify (0,1) for participation of EMPLOYEE in MANAGES Specify (1,1) for participation of DEPARTMENT in MANAGES An employee can work for exactly one department but a department can have any number of employees . Specify (1,1) for participation of EMPLOYEE in WORKS_FOR Specify (0,n) for participation of DEPARTMENT in WORKS_FOR
  • 30. The (min,max) notation relationship constraints Employee Department Manages (1,1) (0,1) Employee Department Works-for (1,N) (1,1)
  • 31. COMPANY ER Schema Diagram using (min, max) notation
  • 32. Relationships of Higher Degree Relationship types of degree 2 are called binary Relationship types of degree 3 are called ternary and of degree n are called n-ary In general, an n-ary relationship is not equivalent to n binary relationships Higher-order relationships discussed further in Chapter 4
  • 33. Data Modeling Tools A number of popular tools that cover conceptual modeling and mapping into relational schema design. Examples: ERWin, S- Designer (Enterprise Application Suite), ER- Studio, etc. POSITIVES: serves as documentation of application requirements, easy user interface - mostly graphics editor support
  • 34. Problems with Current Modeling Tools DIAGRAMMING Poor conceptual meaningful notation. To avoid the problem of layout algorithms and aesthetics of diagrams, they prefer boxes and lines and do nothing more than represent (primary-foreign key) relationships among resulting tables.(a few exceptions) METHODOLGY lack of built-in methodology support. poor tradeoff analysis or user-driven design preferences. poor design verification and suggestions for improvement.
  • 35. Some of the Currently Available Automated Database Design Tools Data modeling, design and reengineering Visual Basic and Visual C++ Visio Enterprise Visio Data modeling, business logic modeling Enterprise Application Suite Sybase Conceptual modeling up to code maintenance Xcase Resolution Ltd. Mapping from O-O to relational model RW Metro Rogue Ware Modeling in UML and application generation in C++ and JAVA Rational Rose Rational Mapping from O-O to relational model Pwertier Persistence Inc. Data, process, and business component modeling Platinum Enterprice Modeling Suite: Erwin, BPWin, Paradigm Plus Platinum Technology Data modeling, object modeling, process modeling, structured analysis/design System Architect 2001 Popkin Software Database modeling, application development Developer 2000 and Designer 2000 Oracle Database administration and space and security management DB Artisan Database Modeling in ER and IDEF1X ER Studio Embarcadero Technologies FUNCTIONALITY TOOL COMPANY
  • 36. ER DIAGRAM FOR A BANK DATABASE © The Benjamin/Cummings Publishing Company, Inc. 1994, Elmasri/Navathe, Fundamentals of Database Systems, Second Edition
  • 37. PROBLEM with ER notation THE ENTITY RELATIONSHIP MODEL IN ITS ORIGINAL FORM DID NOT SUPPORT THE SPECIALIZATION/ GENERALIZATION ABSTRACTIONS
  • 38. Extended Entity-Relationship (EER) Model Incorporates Set-subset relationships Incorporates Specialization/Generalization Hierarchies NEXT CHAPTER ILLUSTRATES HOW THE ER MODEL CAN BE EXTENDED WITH - Set-subset relationships and Specialization/Generalization Hierarchies and how to display them in EER diagrams