Consider the following statements:

A. A database design is in BCNF if each member of the set of relation schemas that constitutes the design is in BCNF

B. A BCNF schema can have transitive dependency

C. It is always possible to obtain a 3NF design without sacrificing a lossless join

D. There are multivalued dependencies in 4NF 

The correct answer is A, C and D only

Key Points

• A. A database design is in BCNF if each member of the set of relation schemas that constitutes the design is in BCNF.
  • This is true. BCNF (Boyce-Codd Normal Form) applies at the relation schema level (a set of attributes); if all relation schemas are in BCNF, the database design can be said to be in BCNF.
• B. A BCNF schema can have transitive dependency.
  • This is false. The definition of BCNF is that for every dependency X -> Y in a relation, X must be a superkey. This disallows transitive dependencies, which would imply that there's a non-superkey attribute that determines another attribute.
• C. It is always possible to obtain a 3NF design without sacrificing a lossless join.
  • This is true. The process of normalizing a database schema to 3NF can be done in such a way that it does not lose the ability to perform a lossless join. This is ensured by taking care that when a functional dependency X -> Y causes a violation, the decomposition of the relation includes X in all decomposed relations.
• D. There are multivalued dependencies in 4NF.
  • This is True. 4NF (Fourth Normal Form) is specifically designed to handled multivalued dependencies. A multivalued dependency always requires at least three attributes because it consists of at least two attributes that are dependent on a third.

Based on these explanations, we can see that only statements A, C and D are true. Therefore, the correct option using the provided choices is: A, C, and D only