dependency preservation

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

Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y...

$$R(A,B,C,D)$$ is a relation. Which of the following does not have a lossless-join, dependency preserving $$BCNF$$ decomposition?

State True or False with reason. There is always a decomposition into Boyce-codd normal form $$(BCNF)$$ that is lossless and dependency preserving.