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

$R=(A,B,C,D)$

$A\to BC, B\to D, D\to B$

The relation $R$ has transitive dependence: $D\to B$ , $B\to D$ .

So, the decomposition with relations in BCNF is:

$R_1=(A,B,C)$

$R_2=(B,D)$

The decomposition is dependency preserving because:

$A\to B, B\to D \implies A\to D$