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

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 2

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? 3

4. Lossless Decomposition & Dependency Preserving R = (A, B, C)F= {A  B, B  C} Is the decomposition of R into R 1 = (A, B) and R 2 = (B, C) lossless? Dependency preserving? How about R 1 = (A, B), R 2 = (A, C)? 4

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? 5

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) 6

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. 7

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