7.22 Give a lossless, dependency-preserving decomposition into 3NF of schema R of Exercise 7.1.

Answer 1

Recall that the schema R of Exercise 7.1 is:

R(A,B,C,D,E)

with the functional dependencies:

A → BC
CD → E
E → A

To decompose R into 3NF, we first check if it is already in 3NF. Since there is only one candidate key (A), and all non-prime attributes (B, C, D, E) depend only on A, R is already in 3NF.

Therefore, the lossless, dependency-preserving decomposition into 3NF of R is simply:

R1(A, B, C)
R2(C, D, E)

where R1 includes the first functional dependency and R2 includes the second and third functional dependencies.