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CS403 - Database Management Systems - Lecture Handout 10

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Overview of Lecture

  • Cardinality Types
  • Roles in ER Data Model
  • Expression of Relationship in ER Data Model
  • Dependency
  • Existence Dependency
  • Referential Dependency
  • Enhancements in the ER-Data Model
  • Subtype and Supertype entities

Recalling from the previous lecture we can say that that cardinality is just an expression which tells us about the number of instances of one entity which can be present in the second relation. Maximum cardinality tells us that how many instance of an entity can be placed in the second relation at most. Now we move onto discuss that what the minimum cardinality is.

Minimum Cardinality:

As the name suggests that the minimum cardinality is the inverse of the maximum cardinality so we can say that the minimum cardinality show us that how many instance of one entity can be placed in another relation at least. In simple words it can be said that the minimum cardinality tells that whether the link between two relations is optional or compulsory. It is very important to determine the minimum cardinality when designing a database because it defines the way a database system will be implemented.

Many to One

Many to One (optional)

Fig 1: Different Cardinalities

In the figure-1 we have one to many cardinality between the entities. Maximum cardinalities are shown with the modifier that appears on the link and is adjacent to the entity rectangle. The other modifier which is next to the maximum cardinality modifier tells the minimum cardinality. The minimum cardinality modifier lies at more distance from the entity as compared to the maximum cardinality modifier.
Determination of the cardinalities is done by interviewing the users of the system and by the analysis of the organization.
The cardinality shown in First Part of the Figure-1 is shown using a relationship between a student and book; this can be a library scenario where students are borrowing books from the library. We can see in the diagram the shape adjacent adjacent to the student entity it shows that the minimum cardinality for the student relationship is zero and maximum cardinality is one. Where as on the other side of the diagram the shape shape 2 adjacent to the book entity show that at most there can be many instances of the book associated with a single instance of student entity, and that there can be at-least no instance associated with the student entity. In general library scenario we can say that one student can borrow at least no and at most many books. Hence the minimum and maximum cardinality is shown.
In the second part of the Figure-1 we see a relationship between the Employee and project entities, the relationship describes one to many association between the project and the employees, It shows that there can be one project having a number of employees, but for the existence of one employee at one project is necessary. So the minimum and maximum cardinality on the project side of the relationship is one, and employees associated with each project can be many at most and none at-least.
Third part of the Figure-1 shows the association between the student and the course entities. Here we can see that the relationship between the student and the course is zero at least and many at most on both the sides of the relationship. The minimum cardinality with zero minimum is also called the optional cardinality. It also shows that one student can have registered more that one subjects and one subject can also be taken by many students. Also it is not necessary for a student to get registered one subject. In the fourth part of the Figure-1 we can see the one to many cardinality between the student and hobby entities the cardinality descriptors show that a student may have no or at most one hobby, but it is worthwhile to notice that the cardinality of the hobby with the student in many but optional, now we can say that one hobby can be associated to nay student but there is a chance that no hobby is associated to one student at a certain time.

Other Notations:

The notation mentioned above is known as crow’s foot notation for the expression of ER-
Diagrams, there can be other notation as well which can be used for creating ER-
Diagrams; one of these notations is shown in the Figure-2. We can see that the one to many cardinality shown in the first part of the diagram is expresses with single and double arrows. The Single arrow in this case shows the one and double arrow show the many cardinality.

Arrow-head notation

Fig. 2: Arrow-head notation

So the First part of the figure-2 show One to many cardinality, second part of the Figure shows many to one and the third part of the cardinality shows many to many cardinality between the entities involved.

Alphabetical notation

Fig. 3: Alphabetical notation

The above Figure shows another notation for creating ER-Diagrams which show that to show the one cardinality we have used 1 and for many cardinality M or N is used.

Dot-based notation

Fig. 4: Dot-based notation

Notations shown in the Figure-4 above as also used for creating ER-Diagrams where 1 is used for showing the single cardinality and the black filled Dot is used for showing many cardinality.

Roles in Relationships

The way an entity is involved in a relationship is called the role of the entity in the relationship. These details provide more semantics of the database. The role is generally clear from the relationship, but in some cases it is necessary to mention the role explicitly.

Two situations to mention the role explicitly

Recursive Relationship:

This is the situation when any attribute of one entity is associated with another attribute of the same entity. Such a link initiates from one entity and terminates on the same entity.

Roles in a unary relationship

Fig-5: Roles in a unary relationship

Figure-5 above shows the recursive relationship which tells that in the faculty of a certain institute we can have one faculty member from among the same faculty as the head of the faculty. Now the role mentioned on the relationship tell that many Faculty instance are headed by one of the entity instance from the same faculty relation.

Multiple Relationships:

This is the second situation which needs the role to be mentioned on the relationship link when there is more than one relationship.

Multiple relationships

Fig. 6: Multiple relationships

As an example we can have a relationship of Faculty members and students as one faculty member may teach a number of students and at the same time one student may have been taught by a number of faculty members. This is one side of the picture. Now on the other side we can say that a faculty member may be supervising a number of students for their final projects. It shows two types of associations between the faculty and the students. So in this type of situation it is necessary to mention the role of the entities involved in the relationship.


Dependency is a type of constraint, for example once we define the cardinality or relationship among two entities it also is a constraint or check that tells that cardinality should be followed while populating data in relations. Similarly the dependency is a constraint. There are a number of dependency types which are expressed below:

The Existence dependency:

This is the type of dependency which exists when one entity instance needs instance of another entity for its existence. As we have seen earlier in case of employee of and organization and the projects associated with the employees there we see that employees are dependent on projects, it means that if no project is assigned to an employee it can not exist. In other words we can say that at a certain time an employee must be working on at least one project.

Identifier Dependency:

It means that the dependent entity incase of existence dependency does not have its own identifier and any external identifier is used to pick data for that entity. And to define a key in this entity the key of the parent entity is to be used in the key for this entity may be used as composite keys.

Referential Dependency:

This is the situation when the dependent entity has it own key for unique identification but the key used to show the reference with the parent entity is shown with the help of an attribute of the parent entity. Means to show the link of the parent entity with this entity there will be an attribute and a record in this entity will not exist without having a record in the parent entity. Despite of having its own identifier attribute.
This type of identifier or attribute in the weak entity is known as foreign key.

Referential Dependency

In the Figure-7 above the relation shown is expression the existence dependency where it is necessary for a book instance to exist if there exist the copies of the book with the same bkId.

Enhancements in E-R Data Model:

The topics that we have discussed so for constitute the basics of ER-Model. The model is further extended and strengthened with addition of some new concepts and modeling constructs, which are discussed below

Super-type and Subtypes

These are also relationships existing between entities, also referred to as generalized and specialized respectively let us examine the figure below to grasp the idea of super-type and subtype.

Super-type and Subtypes

Fig-8 (Super-types and Subtypes)

In the Figure:8 show above there are different levels of existence of entities, at the top level we have general entity type, which are described as having a number of Subtype entities, these sub entities are in-turn acting as supertypes entities for a number of other entities. As we see in case of person supertype we can have further classify the person entity as Student (STD) and Teacher of Faculty member (FAC). Subtype entities are expressed with a link to the supertypes having an arc on the link—the arms of which point to the supertype entity. As we move downward the distributed entities are known as specialized entities.

In the next Lecture the process of Generalization and Specialization will be discussed in detail.


In this lecture we have discussed an important topic of cardinalities and their representation in the E-R data model. For a correct design the correct identification of cardinalities is important.