Question

Consider the relation schema R=(A, B, C, D) with functional dependency F as follows

A BC

B D

D B

Show a decomposition of R into R1 and R2 so that each relation of the decomposition is

in BCNF and also dependency preservation is achieved.

Answer 1

A decomposition {R1, R2} is a lossless-join decomposition if R1 ∩ R2 → R1 or R1 ∩ R2 → R2. Let R1 = (A, B, C), R2 = (A, D, E), and R1 ∩ R2 = A. Since A is a candidate key (see Practice Exercise 8.6), Therefore R1 ∩ R2 → R1.