Consider a Schema R(A,B,C,D) and FD's A --> B and C --> D. Then the decomposition R1(A,B) and R2(C,D) is ....

Answer: dependency preserving but not lossless join

Decomposition of R into R1 and R2 is lossless-join decomposition if at least one of the following functional dependencies is in F+ (Closure of FD’s)

R1 ∩ R2 → R1

             OR

            R1 ∩ R2 → R2

Given relation R(A, B, C, D) is decomposed into R1 (A, B) and R2(C, D), and R1 ∩ R2 is empty. So, the decomposition is not lossless.

Decomposition of R into R1 and R2 is a dependency preserving decomposition if closure of functional dependencies after decomposition is same as closure of of FDs before decomposition.

In given relation R, the FD’s A->B and C->D are preserved after decomposition also.

Refer Properties of Relational decomposition