Consider a schema R and a set F of functional dependencies as follows:R = (A,B,C,D,E).F = {A → BC,CD → E,B →D,E → A}.Determine whether or not the following decomposition of R is a lossless decomposition:R = (A, B, C), R2 = (A, D, E).Show your computational steps as you derive the answer.

To check for lossless join decomposition using functional dependency, the following set of the…

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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Consider a schema R, a set F of functional dependencies on R, and two candidate keys (k1, k2) as follows:R = (X,Y,Z).F = {Y → Z,XZ → Y}.k1 = XZ.k2 =XY Is R in BCNF? Is R in 3NF?(a) R is in both BCNF and 3NF(b) R is in BCNF but not in 3NF(c) R is not in BCNF but in 3NF(d) R is in neither BCNF not 3NF
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 the schema R=ABCDEG and the set of functional dependenciesF={BC→AG, BG→CD, C→AE, D→AG}2a) Determine the keys of the schema2b) Decide whether the schema is 3NF and motivate your answer 2c) Find a decomposition of the schema such that:- every subschema is 3NF- preserves the dependencies- has a lossless join.
Consider the schema R = (A, B, C, D, E, G) and the set F of functional dependencies:AB → CDADE → GDEB → GCG → DEUse the 3NF decomposition algorithm to generate a 3NF decomposition of R,and show your work. This means: A list of all candidate keys.
Consider a relational schema R = {A, B, C, D, E, G, H}, satisfying the functional dependencies F = {E → G, E → H, G → H, A → BC, BC → D, C → H, EG → A}. a) Derive all candidate keys for this schema. b) Derive a canonical cover of the functional dependencies in F. c) Is the above schema in BCNF? Prove or disprove. If it is not in BCNF, convert it into BCNF. d) Is the BCNF schema from (c) dependency-preserving? Prove or disprove. If not, convert into 3NF.
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.
Consider a schema R={A,B,C,D,E} and the following set of functional dependencies: {AB-> C, C->D, D->BE} Is R in Boyce-Codd normal form? Justify your answer.
Consider the schema R = (A, B, C, D, E, G) and the set F of functional dependencies:AB → CDADE → GDEB → GCG → DEUse the 3NF decomposition algorithm to generate a 3NF decomposition of R,and show your work. This means: The remaining steps of the algorithm, with explanation.
Computer Science Given the relation R (A, B, C, D, E, F, G) and the set of functional dependencies: F= {BCD → A, BC → E, A → F, F→G, C→D, A→G}, a) Decompose R into 3NF. Show the different steps. b) Is this decomposition also in BCNF? Why or why not?
Consider the schema R = (A, B, C, D, E, G) and the set F of functional dependencies:AB → CDADE → GDEB → GCG → DEUse the 3NF decomposition algorithm to generate a 3NF decomposition of R,and show your work. This means: The final decomposition.
Consider a relation with schema R(A,B,C,D,E,G) and functional dependencies (FDs) C→D; B→A; D→E; E→G ) What is the closure of {B,C}? Show steps of your solution. Find 2 nontrivial FDs that can be inferred from the given FDs set. Explain how you found them. Propose one key for a given schema and FDs. Explain how you found it.
Consider a relation schema R = {A, B, C, D, E} and its functional dependency set F = {A → BC,CD → E,B →D,E → A}. Let R be decomposed into R1 and R2, where R1 = (A,B,C) and R2 = (A,D,E). Is the decompositionlossless? Is the decomposition dependency preserving? (a) The decomposition is lossless and dependency preserving.(b) The decomposition is neither lossless nor dependency preserving.(c) The decomposition is not lossless but dependency preserving.(d) The decomposition is lossless but not dependency preserving.

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