**Exercise 2: Calculating Canonical Covers and Logical Equivalence for Functional Dependencies**For each of the following relations with given functional dependencies:i. Calculate the canonical cover \( Fc \). Show your work (i.e., steps).ii. Demonstrate that \( Fc \) is logically equivalent to \( F \).### (a) Relation R with Functional Dependencies:- **Relation \( R \):** \((ABCDEFG)\)- **Functional Dependencies \( F \):** \(\{ AB \rightarrow AC, B \rightarrow D, D \rightarrow AE \} \)### (b) Relation R with Functional Dependencies:- **Relation \( R \):** \((ABCDEFG)\)- **Functional Dependencies \( F \):** \(\{ AB \rightarrow CD, CDE \rightarrow AB, AG \rightarrow BD, BDG \rightarrow EF \} \)

NOTE: According to the rules, only question (a) is to be answered (i) Fc is called a canonical cover…

2.For each of the following relations with given functional dependencies, @Calculate canonical cover Fc. Show your work (i.e., steps). (ii) Show that Fc is logically equivalent with F. (a) R=(ABCDEFG), F={AB→AC, B→ D, D→AE}. (b) R=(ABCDEFG), F={AB>CD, CDE→AB, AG→BD, BDG→EF}

2.For each of the following relations with given functional dependencies, @Calculate canonical cover Fc. Show your work (i.e., steps). (ii) Show that Fc is logically equivalent with F. (a) R=(ABCDEFG), F={AB→AC, B→ D, D→AE}. (b) R=(ABCDEFG), F={AB>CD, CDE→AB, AG→BD, BDG→EF}

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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Question

**Exercise 2: Calculating Canonical Covers and Logical Equivalence for Functional Dependencies**

For each of the following relations with given functional dependencies:

i. Calculate the canonical cover \( Fc \). Show your work (i.e., steps).

ii. Demonstrate that \( Fc \) is logically equivalent to \( F \).

### (a) Relation R with Functional Dependencies:
- **Relation \( R \):** \((ABCDEFG)\)
- **Functional Dependencies \( F \):** \(\{ AB \rightarrow AC, B \rightarrow D, D \rightarrow AE \} \)

### (b) Relation R with Functional Dependencies:
- **Relation \( R \):** \((ABCDEFG)\)
- **Functional Dependencies \( F \):** \(\{ AB \rightarrow CD, CDE \rightarrow AB, AG \rightarrow BD, BDG \rightarrow EF \} \)

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