Exercise 3 (Functional Dependencies and Normal Forms) [30 points]

Consider the relation schema R(ABCDEFG) with the functional dependencies A -> B, BD -> CG and AFG -> E.

1. [5 points] Using Armstrongs axioms (6 inference rules), show that the given FDs (functional dependencies) imply that ADF -> E. For each step, indicate which axiom and other FDs youre using.

2. [5 points] List all candidate keys of R. Show each step in detail.

3. [5 points] Suppose we project R onto S(ADFG). Give a minimal cover of FDs that hold in S.

4. [10 points] Let R = ABCDE, R1 = AD, R2 = AB, R3 = BE, R4 = CDE, and R5 = AE. Let the functional dependencies be: A -> C, B -> D, C -> D, DE -> C, CE -> A. Use Chase Test to determine if this is Lossless Join Decomposition.

5. [5 points] Is the FDs of the previous question equivalent to FDs {A -> CD, DE -> A, BE -> C, B -> D}?