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 lossless. For those that are not lossless, 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 B > D.

For each of the sets of FDs above, are dependencies preserved by the decomposition?