Exercise 3.4.1: 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. d) A > D , CD > E , and E ^ D.