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 32E
a.
Explanation of Solution
Nontrivial functional dependency
- The functional dependency CD → AB can also be written as follows:
CD → A
CD → B
- Now, CD+ = {C D A B C E}
- Thus, CD+ contains B without using the functional dependency, CD → B.
- Thus, CD → B can be deleted...
b.
Explanation of Solution
BCNF decomposition
- Here A → BC violates third normal form.
- Hence R(ABCDE) can be decomposed i...
c.
Explanation of Solution
Loseless decomposition
- The common attribute is A in relations R1(ABC) and R2(ADE)...
d.
Explanation of Solution
Dependency preserving decomposition
- The functional dependencies of original relation R is BD → E and CD → AB...
Expert Solution & Answer
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Students have asked these similar questions
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 the relation schema R(A, B, C, D, E, F) and the set S = {AB->C, BC->AD, D->E, C->B) of functional dependencies. Assuming that R is decomposed into the relation schemas R1(A,B), R2(B,C), R3(A,B,D,E) and R4(E,F). Use the Chase test to show if this is a lossless decomposition.
Consider the schema R = (A, B, C, D, E, G) and the set F of functional dependencies:A → BCBD → ECD → AB Find a nontrivial functional dependency containing no extraneous attributes that is logically implied by the above three dependencies and explain how you found it.
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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Similar questions
- Given R ={A, B, C, D}, and the set of Functional dependencies A→BC, B→D. (a) Is the decomposition of R onto R1 ={A, B}and R2 ={B, C, D}lossless? Why? Is it dependency preserving? Why? (b) Is the decomposition of R onto R1 ={A, B}and R2 ={A, C, D}lossless? Why? Is it dependency preserving? Why? (c) Is the decomposition of R onto R1 ={A, B, C}and R2 ={B, D}lossless? Why? Is it dependency preserving? Why?arrow_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 = (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_forward
- Consider the relation R(A, B, C, D, E), and the decomposition of R into R1(ABC) and R2(ADE).(a) Give a set of functional dependencies (FDs) such that the decomposition into R1 andR2 is lossless join and dependency preserving. Justify why your FDs satisfy the criteria.(b) Give a set of functional dependencies such that the decomposition into R1 and R2 islossless join, but not dependency preserving. Justify why your FDs satisfy the criteria.(c) Give a set of functional dependencies such that the decomposition into R1 and R2 isnot lossless join, but dependency preserving. Justify why your FDs satisfy the criteria.arrow_forwardConsider 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.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_forward
- 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.arrow_forwardGiven a relation R( P, Q, R, S, T, U, V, W, X, Y) and Functional Dependencyset FD = { PQ → R, P → ST, Q → U, U → VW, and S → XY}, determine whetherthe given R is in 3NF? If not convert it into 3 NF.arrow_forwardGiven R ={A, B, C}, and the set of Functional dependencies A→B, B→C. (a) Is the decomposition of R onto R1 ={A, B} and R2 ={A, C} lossless? Why? Is it dependency preserving? Why? b) Is the decomposition of R onto R1 ={A, B}and R2 ={B, C}lossless? Why? Is it dependency preserving? Why? (c) Is the decomposition of R onto R1 ={A, C} and R2 ={B, C}lossless? Why? Is it dependency preserving? Why?arrow_forward
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