Question

Suppose each delivery of a course is called a section. In any one term suppose a course may have multiple sections and each section is assigned an instructor. Each course has a course title. Consider a Section relation where the PK is {dept number, course number, section number}. What FDs exist? Is there a partial dependency?

Short answer

The functional dependencies are: 1. {department number, course number} -> {course title} 2. {department number, course number, section number} -> {instructor} 3. {department number, course number} -> {section number}Yes, there is a partial dependency - {department number, course number} -> {course title}.

Step-by-step solution

Recognize the Elements and the Primary Key

From the information given, it seems that the primary key in the Section relation is the combination of the department number, course number and section number. The attributes are: department number, course number, section number, course title, and instructor.

Identify Functional Dependencies

Functional Dependencies (FDs) are the relationships between the attributes of a relation. From the exercise, we can identify three FDs: 1. {department number, course number} -> {course title} 2. {department number, course number, section number} -> {instructor} 3. {department number, course number} -> {section number} The first FD means the department number, and course number uniquely determines the course title. The next FD signifies that the department number, course number, and section number together can specify the instructor. The third FD has the department and course number giving the section number.

Check Partial Dependency

Partial dependency is when a non-prime attribute is functionally dependent on a part (not all) of the primary key. The non-prime attributes here are course title and instructor. From the FDs listed before, it can be observed that {department number, course number} -> {course title} is a partial dependency as course title (a non-prime attribute) depends on part of the primary key ({department number, course number}). On the other hand, {department number, course number, section number} -> {instructor} is not a partial dependency because all parts of the primary key are involved.

Key concepts

Partial Dependency

Partial dependency occurs within a relational database when a non-prime attribute is functionally dependent on part of a composite primary key, rather than the entire key. To illustrate this with the provided exercise, consider the Section relation where the primary key consists of three elements: department number, course number, and section number. A non-prime attribute, such as the course title, displays partial dependency because it is determined solely by the department number and course number, without the need for the section number.

Understanding partial dependency is crucial as it often points to areas where database normalization can be improved to reduce redundancy. For example, the exercise’s relation hints at unnecessary repetition of the course title for different sections of the same course. Recognizing and resolving partial dependencies by segregation into new relations enables a more efficient and logically structured database.

Relation Primary Key

In relational databases, the primary key is a unique identifier for records in a relation and ensures that each record can be precisely distinguished from others. The exercise presents a primary key composed of several attributes: department number, course number, and section number. This composite key is necessary because each section, although identified by a course number within a particular department, may have multiple occurrences and hence requires a distinct section number for unique identification.

The integrity of a primary key is essential for maintaining accurate and reliable relationships within a database. It prevents duplications and creates a straightforward means for other relations to reference the record. Proper selection and definition of the primary key are foundational aspects of data modeling and database design.

Database Normalization

Database normalization is a systematic approach to organizing data within a database in a way that reduces redundancy and improves data integrity. It involves structuring a database in such a way that dependencies among the data are properly enforced. This means dividing larger tables into smaller, stable tables and defining relationships between them appropriately.

Based on the example, database normalization would address the issue of partial dependency by separating the course information into a different table to ensure that each logical piece of data is stored only once. By reducing redundancy, normalization simplifies data management, helps prevent anomalies during data operations (like insertions, deletions, and updates), and often leads to more efficient database schemas. Understanding the levels of normalization, commonly referred to as normal forms, aids database designers in creating relational databases that are efficient, easy to maintain, and scalable.