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 FD's, 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 BCD c) A D, D E, and B-D. d) A-D, CD E, and E-D