1.Consider the following collection of relations and dependencies. As-sume that each relation is obtained through decomposition from a relation with at-tributes ABCDEFGHI and that all the known dependencies over relation ABCDEFGHI are listed for each question. (The questions are independent of each other, obviously, since the given dependencies over ABCDEFGHI are di?erent.) For each (sub)relation: (a) State the strongest normal form that the relation is in. (b) If it is not in BCNF, decompose it into a collection of BCNF relations.
1. R1(A,C,B,D,E), A → B, C → D
2. R2(A,B,F), AC → E, B → F
3. R3(A,D), D → G, G → H
4. R4(D,C,H,G), A → I, I → A
5. R5(A,I,C,E)
2.Consider the relation shown in Figure 19.1.
1. List all the functional dependencies that this relation instance satis?es.
2. Assume that the value of attribute Z of the last record in the relation is changed from z3 to z2. Now list all the functional dependencies that this relation instance satis?es.
X Y Z
x1 y1 z1
x1 y1 z2
x2 y1 z1
x2 y1 z3