Exercise 13: Identifying Lossless-Join and Dependency-preserving Decompositions

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}, {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.

  1. B → E, CE → A
  2. AC → E, BC → D
  3. A → D, D → E, B → D
  4. A → D, CD → E, E → D

Exercise 3.4.2

For each of the sets of FD’s in Exercise 3.4.1, are dependencies preserved by the decomposition?