Week 12 Discussion

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Dec 6, 2023

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Closure of a Set of Functional Dependencies In the context of relational databases, the closure of a set, often referred to as the "functional dependency closure" or simply "closure," is a fundamental concept that plays a crucial role in database design and normalization. The closure of a set of functional dependencies represents the comprehensive collection of all functional dependencies that can be logically deduced or implied from the given set. It serves as a powerful tool for understanding the underlying relationships between attributes within a database schema, enabling database designers to ensure data integrity, reduce redundancy, and optimize the structure of their relational databases. By systematically deriving all possible dependencies, the closure provides a clear and formalized way to uncover the intrinsic relationships that govern the organization of data in a relational database. The following example is from an article by Nisha (n.d.). Consider a relation R with attributes A, B, C, D, E, F, and G, and the following set of functional dependencies: A → BC, BC → DE, D → F, and CF → G. We can find the closure of various attributes and attribute sets within this relational schema. Closure of attribute A: A+ = {A} (trivial) A+ = {A, B, C} (using A → BC) A+ = {A, B, C, D, E} (using BC → DE) A+ = {A, B, C, D, E, F} (using D → F) A+ = {A, B, C, D, E, F, G} (using CF → G) Thus, the closure of attribute A is A+ = {A, B, C, D, E, F, G}.
Closure of attribute D: D+ = {D} (trivial) D+ = {D, F} (using D → F) We cannot determine any other attributes using attributes D and F. Thus, D+ = {D, F}. Closure of attribute set {B, C}: {B, C}+ = {B, C} (trivial) {B, C}+ = {B, C, D, E} (using BC → DE) {B, C}+ = {B, C, D, E, F} (using D → F) {B, C}+ = {B, C, D, E, F, G} (using CF → G) Hence, the closure of the attribute set {B, C} is {B, C, D, E, F, G}. References Elmasri, R., & Navathe, S. B. (2015). Fundamentals of Database Systems (7th ed.). Pearson Education (US). https://reader2.yuzu.com/books/9780133971224 Nisha, C. D. (n.d.). DBMS : Closure properties - little flower college. https://littleflowercollege.edu.in/upload/e_contents/files/187d8c7967172ef5cc75d9b2a70 9d6cf.pdf
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