Suppose you are given a relation R(A,B,C,D). For each of the following set of FDs, assuming they are the only dependenci

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Suppose you are given a relation R(A,B,C,D). For each of the
following set 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 -> D, 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.