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}. Consider the following five sets of FDs:

(a) B E and CE A

(b) AC E and BC D

(c) A D, D E, and B D

(d) A D, CD E, and E D

(e) A B, BC D, and E B

For each set 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 tuples than R has when projected onto the decomposed relations and rejoined.