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Understanding Functional Dependencies and Normalization in Database Design

In this exercise, we explore the concepts of functional dependency, attribute closure, and normalization in database design using a specific schema R = (A, B, C, G, H, I). We prove various functional dependencies and compute attribute closures to determine candidate keys. The exercise also covers lossless decomposition and whether specific decompositions preserve dependencies. We analyze Boyce-Codd Normal Form (BCNF) and Third Normal Form (3NF) to assess the normalization status of given relations. Finally, we find a minimal cover for a set of functional dependencies (FDs).

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Understanding Functional Dependencies and Normalization in Database Design

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  1. CSCI 4333 Database Design and Implementation – Exercise (3) Xiang Lian The University of Texas – Pan American Edinburg, TX 78539 lianx@utpa.edu

  2. Functional Dependency • Given a schema R= (A, B, C, G, H, I) and a set of functional dependencies: F= {A  B A  C CG  H CG  I B  H} • Please prove that the following functional dependencies are in F+: A  H AG  I CG  HI

  3. Attribute Closure • Given a schema R= (A, B, C, G, H, I)and a set of functional dependencies: F= { A  B A  C CG  H CG  I B  H} • Please compute attribute closure (AG)+ • Is AG a candidate key?

  4. Lossless Decomposition & Dependency Preserving • R = (A, B, C) F= {A  B, B  C} • Is the decomposition of R into R1= (A, B) and R2 = (B, C) lossless? Dependency preserving? • How about R1 = (A, B), R2 = (A, C)?

  5. Boyce-Codd Normal Form (BCNF) • R = (A, B, C)F = {A  B B  C} • Is R in BCNF? Why? (Hint: Key = {A}) • How to decompose R if R is not in BCNF?

  6. Third Normal Form (3NF) • R = (J, K, L)F = {JK  L, L  K} • Is R in 3NF? Why? (Hint: Two candidate keys: JK and JL)

  7. Minimal Cover • Find a minimal cover of the following set of FDs: • ABCD • BCFG • AG • GB • CG • Is the decomposition of ABCDFG into ABCD and ACFG lossless? Explain.

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