Consider a schema $R(A,B,C,D)$ and functional dependencies $A \rightarrow B$ and $C \rightarrow D$. Then the decomposition of R into $R_1 (A,B)$ and $R_2(C,D)$ is
- dependency preserving and lossless join
- lossless join but not dependency preserving
- dependency preserving but not lossless join
- not dependency preserving and not lossless join