CSCI 6315 Applied Database Systems – Exercise (5) Xiang Lian The University of Texas Rio Grande Valley Edinburg, TX 78539 xiang.lian@utrgv.edu

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

Attribute Closure Please compute attribute closure (AG)+ 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?

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)?

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?

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)

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.