Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Expert Solution & Answer
Chapter 7, Problem 33E
a.
Explanation of Solution
Candidate keys
- A key is known as a candidate key when it has the ability to derive all the attributes from a relation...
b.
Explanation of Solution
Canonical cover for F
- The steps for canonical conversion is to break the functional dependencies so that right hand side will have only one single attribute.
- Then all the extra unnecessary functional dependencies are removed.
- Then all the functional dependencies are combined.
- Hence here the given functional dependencies include AB -> G, AB -> D ...
c.
Explanation of Solution
Remaining steps of
- The given relation is in 1NF as there is no multivalued attribute or complex attribute.
- The given relation is not in 2NF as there is partial functional dependency...
d.
Explanation of Solution
Final decomposition
- Given functional dependencies are AB -> CD, ADE -> GDE, B -> GC, G -> DE.
- Here ADE -> GDE have some trivial attributes.
- So those attributes can be removed and hence the dependency is ADE -> G...
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Students have asked these similar questions
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 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.
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.
Chapter 7 Solutions
Database System Concepts
Ch. 7 - Prob. 1PECh. 7 - Prob. 2PECh. 7 - Explain how functional dependencies can be used to...Ch. 7 - Prob. 4PECh. 7 - Prob. 5PECh. 7 - Prob. 6PECh. 7 - Prob. 7PECh. 7 - Prob. 8PECh. 7 - Prob. 9PECh. 7 - Prob. 10PE
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Explain what is meant by repetition of...Ch. 7 -
Why are certain functional dependencies called...Ch. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Prob. 28ECh. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - Prob. 38ECh. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43E
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- Consider the schema R = (A, B, C, D, E, G, H) and the set F of functional dependencies:AB → CDD → CDE → BDEH → ABAC → DCUse the 3NF decomposition algorithm to generate a 3NF decomposition of R,and show your work. This means: The steps of the algorithm, with explanation.arrow_forwardSuppose 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 → Aarrow_forwardConsider 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.arrow_forward
- 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 3NFarrow_forwardConsider 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.arrow_forwardConsider 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.arrow_forward
- 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?arrow_forwardConsider the schema R = (A, B, C, D, E, G) and the set F of functional dependencies:A → BCBD → ECD → AB For your decomposition, state whether it is dependency preserving and explain why ?arrow_forwardConsider 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.arrow_forward
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