Question 1. Consider a relation R(A, B, C, D, E) with the following functional dependency set F = {AB -> C, CD -> E, DE -> B}

[Read an f.d XY -> Z as {X, Y} -> {Z} where X, Y, and Z are atomic attributes.]

(i) Test whether AB is a candidate key of R. (Show your work).

(ii) Find a candidate key (possibly another) of R. (Show your work)

Question 2. Consider a relation R(A, B, C, D) with the functional dependencies {AB -> C, C -> D, D -> A}. Does BC -> A hold on R? Explain

Question 3. Consider the following relation:

R (Doctor#, Patient#, Date, Diagnosis, Treat-code, Charge)

In this relation, a tuple describes a visit of a patient to a doctor along with a treatment code and daily charge. Assume that diagnosis is determined (uniquely) for each patient by a doctor. Assume that each treatment code has a fixed charge (regardless of patient).

(i) What are the functional dependencies that can be inferred from the above?

(ii) Is this relation in 2NF? Justify your answer and decompose if necessary.

(iii) Argue whether further normalization to 3NF is necessary, and if so, perform it.

Question 4. Consider the universal relation R(A, B, C, D, E, F, G). The following dependencies hold on R: {A -> CDE, B -> FG, AB -> CDEFG}. Find a minimal cover of the functional dependency set. (Note: If you end up with fds like A B, A C, A E, then you can combine them into single fd as A -> BCE. That is, it is okay to combine dependencies with same left-hand side after ending the algorithm.)