Exercise 19.10 Suppose you are given a relation R(A,B,C,D). For each of the following sets of FDs, assuming they are the only dependencies that hold for R, do the following: (a) Identify the candidate key(s) for R. (b) State whether or not the proposed decomposition of R into smaller relations is a good decomposition and briefly explain why or why not.
1. B → C, D → A; decompose into BC and AD.
2. AB → C, C → A, C → D; decompose into ACD and BC.
3. A → BC, C → AD; decompose into ABC and AD.
4. A → B, B → C, C → D; decompose into AB and ACD.
5. A → B, B → C, C → D; decompose into AB, AD and CD.
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