Which of the following statements is true for dependency preserving…

Correct answer: Both of the first two statements are true.

• The statement "It allows us to enforce all FDs on the decomposed relations."

  Explanation: Dependency preservation means the projected functional dependencies on the decomposed relations are sufficient to enforce the original functional dependencies without needing to rejoin the decomposed relations.

• The statement "It ensures that every FD is preserved in at least one of the decomposed relations."

  Explanation: Each original functional dependency must be implied by the union of the projected dependencies on the decomposed schemas, so every FD can be checked within some decomposed relation.

Note: The statement "It guarantees lossless join property." is not necessarily true. Dependency preservation and lossless join are separate properties; a decomposition can preserve dependencies but be lossy. Both properties are desirable and should be checked independently.

How to check dependency preservation:

• Project the full set of functional dependencies onto each decomposed schema.

• Take the union of those projected dependencies and verify that this union implies the original set of functional dependencies (i.e., the original FDs are in the closure). If so, the decomposition is dependency preserving.