Exercise 19.8 Consider the attribute set R = ABCDEGH and the FD set F = {AB → C, AC → B, A...

Exercise 19.8 Consider the attribute set R = ABCDEGH and the FD set F = {AB → C, AC → B, AD → E, B → D, BC → A , E → G}.

1. For each of the following attribute sets, do the following: (i) Compute the set of dependencies that hold over the set and write down a minimal cover. (ii) Name the strongest normal form that is not violated by the relation containing these attributes. (iii) Decompose it into a collection of BCNF relations if it is not in BCNF.

(a) ABC, (b) ABCD, (c) ABCEG, (d) DCEGH, (e) ACEH

2. Which of the following decompositions of R = ABCDEG, with the same set of dependencies F, is (a) dependency-preserving? (b) lossless-join?

(a) {AB, BC, ABDE, EG}

(b) {ABC, ACDE, ADG}