1. CSCI 4333 Database Design and Implementation – Exercise (3)
Xiang Lian
The University of Texas Rio Grande Valley
Edinburg, TX 78539

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 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?

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.