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 36E
Explanation of Solution
BCNF (Boyce Codd Normal Form):
A relation is said to be in BCNF if it holds the following 2 conditions:
- The relation is in Third Normal Form
- For every dependency X→a, X is superkey.
Every binary relation which means every schema consisting of exactly 2 attributes is said to be in BCNF.
In order to prove that, consider all possible combinations of functional dependencies on a relation R with 2 attributes A1 and A2.
Case1: A1→A2
In this case, A1 is the candidate key and hence also a superkey as candidate keys is minimal superkeys.
So, the BCNF condition satisfies in this case...
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Students have asked these similar questions
Show that every schema consisting of exactly two attributes must be in BCNF regardless of the given set F of functional dependencies.
Consider 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 ?
Define the terms "normalization" and "functional dependence" as they apply to 1nf, 2nf, and 3nf.
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 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.arrow_forwardConsider schema(R, F), where R=ABCDE, F={D→EB, E→A, AC→D, BD→E} Decompose the schema into a set of BCNF schemas. Is this decomposition lossless? Is it dependency-preserving? Explainarrow_forwardIf the issue set consists entirely of nominal characteristics, a vector space-based classification approach is not the best option. Please share your thoughts on this assertion. How would you apply ML to the task of categorizing nominal data?arrow_forward
- 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.arrow_forwardc. For a schema R (A, B, C, D) bearing FDs F={A → B, B + c, C + D,D + A}, find if the decomposition of R into R1 (A, B, C) and R2 (B, c, D) is dependency preserving?arrow_forwardWhat is the function of a ModelGen operator? A It identifies fundamental conflicts and devises rules for resolving them. B It takes a model in one meta-model and translates it into another meta-model. (C) It transforms the data from one data model to another and applies a schema mapping. D It transforms data from the model and schema in which it is stored into the target message format.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_forwardWhat is the relationship between the Third Normal Form (3NF) and the Boyce Codd Normal Form (BCNF)? (a) 3NF and BCNF are equivalent.(b) If a schema is in 3NF, it is also in BCNF.(c) If a schema is in BCNF, it is also in 3NF.(d) If a schema is in 3NF, it is not in BCNF.(e) none of the above.arrow_forwardWhen the issue set consists entirely of nominal characteristics, vector space-based classification algorithms are often not the best option. Your thoughts on this assertion? How would you use ML to the task of categorizing nominal data?arrow_forward
- It is possible to have a schema and a decomposition that were not produced by the process, are in BCNF, and are not lossless despite the BCNF method's assurance of lossless decomposition. Describe how a schema like this is broken down and provide an example.arrow_forwardEvery SuperKey is a key but not vice versa True False In Relational database modeling, any complex attribute (multi-valued composite or composite with multi-valued component) Can be Directly represented as is without limitations or changes to be done True False Predicate-defined subclasses refers to the classification process of entities in to subclasses based on a conditional value for an attribute, and is shown in an ERD/EERD on the arc connecting the subclass to the specialization bubble True Falsearrow_forwardConsider 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.arrow_forward
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