Question: Let R(A,B,C,D,E) be decomposed into relations with the following three sets of attributes: {A,B,C}, {B,C,D}, and {A,C,E}. For each of the following sets of FDs,

Let R(A,B,C,D,E) be decomposed into relations with the following three sets of attributes: {A,B,C}, {B,C,D}, and {A,C,E}. For each of the following sets of FDs, use the chase test to tell whether the decomposition of R is loosless. For those that are not loosless, give an example of an instance of R that returns more than R when projected onto the decomposed relations and rejoined:

a) B-> E and CE ->A

b) AC ->E and BC ->D

c) A ->D, D ->E, and E ->D

d) A ->D, CD ->E, and E ->D.

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