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Chapter 10: Problem 11

What is a minimal set of functional dependencies? Does every set of dependencies have a minimal equivalent set? Is it always unique?

Short Answer

Expert verified
A minimal set of functional dependencies is a set where no dependency can be discarded without changing the set's closure and each dependency has exactly one attribute on the right side. Yes, every set of dependencies has an equivalent minimal set preserving the constraints of the original set. The minimal equivalent set, however, may not be unique.

Step by step solution

01

Define Minimal Set of Functional Dependencies

A minimal set of functional dependencies is a set of dependencies that has no redundancy. This means that no dependency in the set can be discarded without changing the closure of the set. Additionally, in a minimal set, each dependency has a right side that contains exactly one attribute.
02

Check for Equivalent Minimal Set

Every set of dependencies has an equivalent minimal set. An equivalent set is a set that enforces the same constraints on data as the original set. If the set in question is not minimal, it can be reduced to a minimal set by applying reduction algorithms while maintaining the constraints enforced by the original set.
03

Discuss Uniqueness

The minimal equivalent set for a given set of functional dependencies is not always unique. Different minimal sets can impose the same constraints on the data set. This happens if there are multiple ways to express the same constraints with different combinations of dependencies. Hence, while every set of functional dependencies has a minimal set, that set is not necessarily unique.

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Most popular questions from this chapter

What undesirable dependencies are avoided when a relation is in \(2 \mathrm{NF}\) ?

What is meant by the closure of a set of functional dependencies? Illustrate with an example.

Why should nulls in a relation be avoided as far as possible? Discuss the problem of spurious tuples and how we may prevent it.

Suppose that we have the following requirements for a university database that is used to keep track of students' transcripts: a. The university keeps track of each student's name (SNAME), student number (SNUM), social security number (SSN), current address (SCADDR) and phone \((\mathrm{SCPHONE}),\) permanent address \((\mathrm{SPADDR})\) and phone \((\mathrm{SPPHONE}),\) birth date \((\mathrm{BDATE})\) \(\operatorname{sex}(\operatorname{sex}), \text { class (cLass) (freshman, sophomore, } \ldots, \text { graduate }),\) major depart ment (MAJORCODE), minor department (MINORCODE) (if any), and degree program \(\left(p_{R O C}\right)(B, A,, B, S, \ldots, P H, D,) .\) Both sss \(N\) and student number have unique val. ues for each student. b. Each department is described by a name (DNAME), department code (DCOOE), office number (DOFFICE), office phone (DPHONE), and college (DCOLLECE). Both name and code have unique values for each department. c. Each course has a course name (cNAME), description (cDESC), course number (CNUM), number of semester hours (cREDIT), level (LEVEL), and offering depart. ment (coept). The course number is unique for each course. d. Each section has an instructor (INAME), semester (SEMESTER), year (YEAR), course (seccourse), and section number (secwum). The section number distinguishes different sections of the same course that are taught during the same semester/ year; its values are \(1,2,3, \ldots,\) up to the total number of sections taught during each semester. e. \(A\) grade record refers to a student \((\operatorname{ss} N),\) a particular section, and a grade \((\mathrm{CRADE})\) Design a relational database schema for this database application. First show all the functional dependencies that should hold among the attributes. Then design relation schemas for the database that are each in \(3 \mathrm{NF}\) or BCNF. Specify the key attributes of each relation. Note any unspecified requirements, and make appropriate assumptions to render the specification complete.

What does the term unnormalized relation refer to? How did the normal forms develop historically from first normal form up to Boyce-Codd normal form?
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