1. CSCI 6315 Applied Database Systems – Exercise (4)
Xiang Lian
The University of Texas Rio Grande Valley
Edinburg, TX 78539

2. Attribute Closure and Entailment
If X = {AB} and F = {AD, BCEJ, BDAE, EJG, ADEH, HDJ}, what is XF+?
Are the FDs ABC and AEG entailed by F?

3. Derivation with Armstrong's Axioms
Using only Armstrong's axioms and the FDs
(a) ABC
(b) ABE
(c) CD
Give a complete derivation of the FD AD.

4. BCNF R={B, C, E} F={EB, BCE} What are candidate keys in R?
Is R in BCNF? If not, how to decompose R losslessly?
BC, EC

5. 3NF
Given R= {BCDFGH} with a set of FDs F={BGCD, GF, CDGH, CFG, FD}
Use the 3NF algorithm to obtain a lossless, dependency-preserving decomposition into 3NF.