COMP353/1 Assignment 3 Functional Dependencies

COMP353/1 Assignment #3

Exercise #1 (10 points)
Here are the two sets of FDs for R {A, B, C, D, E}.
S = {A->B AB->C D->AC D->E} T = {A->BC D->AE}
Are they equivalent?

Exercise #2 (10 points)
Consider the following decomposition of the table ENROLLMENT in two tables Student and Course.

Table ENROLLMENT
StudentID StudentName CourseName Credits
1111111 William Smith COMP218 4
2222222 Michel Cyr COMP353 4
3333333 Charles Fisher COMP348 4
4444444 Patricia Roubaix COMP353 4
2222222 Paul Paul COMP352 3
5555555 Lucie Trembaly COMP354 3

Table Student
StudentID StudentName Credits
1111111 William Smith 4
2222222 Michel Cyr 4
3333333 Charles Latan 4
4444444 Patricia Roubaix 4
2222222 Paul Paul 3
5555555 Lucie Trembaly 3

Table Course
Credits CourseName
4 COMP218
4 COMP353
4 COMP348
4 COMP353
3 COMP352
3 COMP354

Question: Is this decomposition lossless? Justify.

Exercise #3 (15 points)
Using the Functional Dependencies,
F = {A → BC ; CD → E ; B→D ; E→A}

a) Compute the closure of F (F+).
b) Is true / false : F ⊨  E → BC?
c) Provide the minimal cover Fc (min(F)) using steps shown in the class.
d) List of the candidate keys for R

Exercise #4 (15 points)
Consider the relation R(S, N, R, C, J, H, L) and the set of dependencies.
F = {S, N  C ; J, H, C  L ; J, H, L  S, N, R ; S, N, R  J, H, L}.
Prove that F ⊨ J, H, S, N  R using the Armstrong’s axioms?