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