CSCI 5333.4 DBMS
Homework #7

Due date: 11/16 at the beginning of the class.

(1) Use Armstrong's axioms and rules to prove that

F = {A-> BC, BD->C, AC->D}

implies A->D.

(2) Consider R(A,B,C,D) with

F = {A-> BC, BD->C, AC->D}

(a) What are A+, B+, C+ and D+?

(b) What are the candidate keys? Why?

(c) Show all prime attributes and non-prime attributes?

(d) Give a canonical cover of F?

(e) What is the highest normal form (up to BCNF) of R? Why?

(f) If R is not in BCNF, can you provide a lossless FD preserving decompositions of R into BCNF relations?

(3) Consider R(A,B,C,D,E,F) with

F= {A->C, CD->B, BC->E, EF->AB, AB->E, AB->F, ABC->D}

(a) What are A+, B+, C+, D+, E+, F+ and (BC)+?

(b) What are the candidate keys? Why?

(c) Show all prime attributes and non-prime attributes?

(d) Give a canonical cover of F?

(e) What is the highest normal form (up to BCNF) of R? Why?

(f) If R is not in BCNF, can you provide a lossless FD preserving decompositions of R into BCNF relations?

(4) A relation R has two or more attributes. A canonical cover of the set of FD for R has only one non-trival FD. Can yon infer that R in BCNF? Prove your assertion.

(5) Consider R(A,B,D) with a set of applying FDs, F. What is the maximum number of FDs in F, counting both trivial and non-trivial FD, but not counting non-trivial FD with {} in it.

(6) Consider R(A,B,C,D,E) with {A->B, CD->E, BC-> A, BD->CE, ABD-> C}

It is decomposed into R1(A,B,C), R2(B,C,D) and R3(B,D,E).

Is the decomposition lossy? Show your reasoning.