**Exercise 3.3.1:**For each of the following relation schemas and sets of FD's (Functional Dependencies):a) \( R(A, B, C, D) \) with FD's \( AB \rightarrow C \), \( C \rightarrow D \), and \( D \rightarrow A \).b) \( R(A, B, C, D) \) with FD's \( B \rightarrow C \) and \( B \rightarrow D \).c) \( R(A, B, C, D) \) with FD's \( AB \rightarrow C \), \( BC \rightarrow D \), \( CD \rightarrow A \), and \( AD \rightarrow B \).d) \( R(A, B, C, D) \) with FD's \( A \rightarrow B \), \( B \rightarrow C \), \( C \rightarrow D \), and \( D \rightarrow A \).**3.4. DECOMPOSITION: THE GOOD, BAD, AND UGLY**e) \( R(A, B, C, D, E) \) with FD's \( AB \rightarrow C \), \( DE \rightarrow C \), and \( B \rightarrow D \).f) \( R(A, B, C, D, E) \) with FD's \( AB \rightarrow C \), \( C \rightarrow D \), \( D \rightarrow B \), and \( D \rightarrow E \).**Do the following:**i) Indicate all the BCNF (Boyce-Codd Normal Form) violations. Consider FD's not explicitly listed if they follow from given ones, but do not include violations with multiple attributes on the right side.ii) Decompose the relations, as needed, into collections of relations that satisfy BCNF.

3.4. DECOMPOSITION: THE GOOD, BAD, AND UGLY e) R(A, B, C, D, E) with FD's AB → C, DE → C, and B → D. f) R(A, B, C, D, E) with FD's AB → C, C → D, D → B, and D → E. do the following: 93 i) Indicate all the BCNF violations. Do not forget to consider FD's that are not in the given set, but follow from them. However, it is not necessary to give violations that have more than one attribute on the right side. ii) Decompose the relations, as necessary, into collections of relations that are in BCNF.

3.4. DECOMPOSITION: THE GOOD, BAD, AND UGLY e) R(A, B, C, D, E) with FD's AB → C, DE → C, and B → D. f) R(A, B, C, D, E) with FD's AB → C, C → D, D → B, and D → E. do the following: 93 i) Indicate all the BCNF violations. Do not forget to consider FD's that are not in the given set, but follow from them. However, it is not necessary to give violations that have more than one attribute on the right side. ii) Decompose the relations, as necessary, into collections of relations that are in BCNF.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Concepts in Designing Database

A database design is the process of data organization based on a database model. The process deals with identifying what data should be stored in a database and how data elements relate to each other.

Entity Relationship Diagram

Complex real-world applications call for large volumes of data. Therefore, it is necessary to build a great database to store data safely and coherently. The ER data model aids in the process of database design. It helps outline the structure of an organization’s database by understanding the real-world interactions of objects related to the data. For example, if a school is tasked to store student information, then analyzing the correlation between the students, subjects, and teachers would help identify how the data needs to be stored.

Question

**Exercise 3.3.1:**

For each of the following relation schemas and sets of FD's (Functional Dependencies):

a) \( R(A, B, C, D) \) with FD's \( AB \rightarrow C \), \( C \rightarrow D \), and \( D \rightarrow A \).

b) \( R(A, B, C, D) \) with FD's \( B \rightarrow C \) and \( B \rightarrow D \).

c) \( R(A, B, C, D) \) with FD's \( AB \rightarrow C \), \( BC \rightarrow D \), \( CD \rightarrow A \), and \( AD \rightarrow B \).

d) \( R(A, B, C, D) \) with FD's \( A \rightarrow B \), \( B \rightarrow C \), \( C \rightarrow D \), and \( D \rightarrow A \).

**3.4. DECOMPOSITION: THE GOOD, BAD, AND UGLY**

e) \( R(A, B, C, D, E) \) with FD's \( AB \rightarrow C \), \( DE \rightarrow C \), and \( B \rightarrow D \).

f) \( R(A, B, C, D, E) \) with FD's \( AB \rightarrow C \), \( C \rightarrow D \), \( D \rightarrow B \), and \( D \rightarrow E \).

**Do the following:**

i) Indicate all the BCNF (Boyce-Codd Normal Form) violations. Consider FD's not explicitly listed if they follow from given ones, but do not include violations with multiple attributes on the right side.

ii) Decompose the relations, as needed, into collections of relations that satisfy BCNF.

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