Consider a schema R and a set F of functional dependencies as follows:R= (A,B,C,D,E,G).F = {A → BCD, BC DE,B→D,D→A}.Prove that AG is a superkey for R.

First of all , let’s understand what is super key. Super key : Super key can be defined as an…

Answered: Consider a schema R and a set F of…

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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Suppose that we decompose the schema R = (A, B, C, D, E) into (A, B, C) (A, D, E). Show that this decomposition is a lossless decomposition if the following set F of functional dependencies holds: A → BC CD → E B → D E → A
Consider a relation schema R(A, B, C, D, E, G) and a set of functional dependencies F = {A → C, AD → CE, B → ACD, C → B}. (a) Show the steps of computing a canonical cover for F. (b) Compute the closure of AG and then determine whether or not AG is a candidate key. (c) Determine whether or not (A, E, G) is in BCNF and justify your answer using the transitive closure of a set of attributes. If (A, E, G) is not in BCNF, find a BCNF decomposition of it. (d) Assume that (A, E, G) is decomposed into (A, G) and (E, G). Given the above functional dependencies, is this decomposition always lossless? If so, prove this. Otherwise, explain it using an example (i.e., a case of decomposing a table containg rows and columns into two tables). (e) Assume that R is decomposed into R1(A, B, C, D) and R2(A, E, G). Is this decomposition dependency preserving? Justify your answer.
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Consider a schema R and a set F of functional dependencies as follows: R= (A,B,C,D,E,G). F = {A → BCD, BC DE,B→D,D→A}. Prove that AG is a superkey for R.