Reference no: EM132494138

Question 1 Suppose a relation, R = (A,B,C,D,E ) with the following functional dependencies:

{CE → D, D→ B, C →A}

a. Find all candidate keys.

b. Identify the best normal form that R satis?es (1NF, 2NF, 3NF, or BCNF).

c. If the relation is not in BCNF, decompose it until it becomes BCNF.

At each step, identify anew relation, decompose and re-compute the keys and the normal forms they satisfy.

Question 2

A relation R=(A,B,C,D,E) has following functional dependencies:

BD →E, A →C

Show that the decomposition into R1=(A,B,C) and R2=(D,E) is lossy.

Question 3

A set of functional dependencies for a relation R(A,B,C,D,E,F),

F = {AB → C,DC → AE,E → F }

a. What are the keys of this relation?

b. Is this relation in BCNF? If not, explain why by showing one violation.

c. Is the decomposition (A,B,C,D) (B,C,D,E,F) a dependency preserving decomposition? If not, explain brie?y.

Question 4

A set of functional dependencies for a relation R(A,B,C,D,E,F,G),

F = {AD → BF,CD → EGC,BD → F,E → D,F → C,D → F }

a. Find the minimal cover for the above set of functional dependencies.

b. Using the functional dependencies that you computed in step a, ?nd the keys for this relation. Is it in BCNF? Explain.