In the context of relational database normalization, which of the following statements is/are true?

Let us analyze each statement regarding relational decompositions:

• Option A is true: A dependency-preserving and lossless-join decomposition into 3NF is always achievable using the standard synthesis algorithm (Bernstein's algorithm).

• Option B is true: Any relation can always be decomposed into 1NF while preserving all functional dependencies (in fact, a single table with atomic attributes trivially satisfies 1NF and preserves all dependencies).

• Option C is true: While a lossless-join decomposition into BCNF is always possible, it is not always possible to preserve all functional dependencies in BCNF (e.g., in a relation $R(A, B, C)$ with functional dependencies $AB \to C$ and $C \to B$).

• Option D is false: It is always possible to obtain a dependency-preserving decomposition in 2NF (since 3NF decomposition is always dependency-preserving, and any 3NF relation is already in 2NF).

Therefore, the correct options are A, B, and C.