1

CSCI 4333 Database Design and Implementation – Exercise (3)

Xiang Lian

The University of Texas – Pan American

Edinburg, TX 78539

lianx@utpa.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 HAG ICG HI

2

Attribute Closure

• Given a schema R = (A, B, C, G, H, I) and a set of functional dependencies:

F = { A BA C CG HCG IB H}

• Please compute attribute closure (AG)+

• Is AG a candidate key?

3

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)?

4

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

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

Minimal Cover

• Find a minimal cover of the following set of FDs:– ABCD– BCFG– AG– GB– CG

• Is the decomposition of ABCDFG into ABCD and ACFG lossless? Explain.

7

8