Instructions

Functional Dependencies

Show all the working. Do not simply write answers. If essential steps, such as edge diagrams, transitive inferences are missing, points will be deducted.

A-1 Transitive Dependency and Keys (5 points)

You have a relation R(L,M,N,O,P,Q) and a set of functional dependencies F = {LNOM, MNLOP, NO, OPLN}.

[2pt] Can we infer NP LM from F ?

[3pt] Can we infer NQ LO from F ?

A-2 Keys (10 points)

(i) [5pt] Find all the candidate keys of the Relation R(ABCDE) with FD's:

D C, CE A, D A, and AE D

(ii) [5pt] Determine all the candidate and superkeys of the relation R(ABCDEF) with FD's:

AEF C, BF C, EF D, and ACDE F

A-3 Minimal Cover (10 points)

[10 pt] Find all minimal covers for the following set F of functional dependencies.

X Z, XY Z, Z UT, ZU T, ZW XY, WT Z

Show your working clearly. Points will be deducted if you do not show the extraneous attributes, and their elimination.

A-4 Equivalence (15 points)

[15pt] Consider the following set of F.Ds. Determine if FD1 is equivalent to FD2 or to FD3:

FD1:

{BC->D, ACD->B, CG->B, CG->D, AB->C, C->A,D->E,BE->C,D->G,CE->A,CE->G}

FD2:

{AB->C,C->A,BC->D,CD->B,D->E,D->G,BE->C,CG->D}

FD3:

{AB->C,C->A,D->G,BE->C,CG->D,CE->G,BC->D,CD->B,D->E}

You must show closure of each LHS attributes on the left hand side of each FD_i where i = {1,2,3} via going through the other FD set.

Then establish the equivalence.