Briefly answer the following questions:
1. Define the term functional dependency.
2. Why are some functional dependencies called trivial?
3. Give a set of FDs for the relation schema R(A,B,C,D) with primary key AB under which R is in 1NF but not in 2NF.
4. Give a set of FDs for the relation schema R(A,B,C,D) with primary key AB under which R is in 2NF but not in 3NF.
5. Consider the relation schema R(A,B,C), which has the FD B → C. If A is a candidate key for R, is it possible for R to be in BCNF? If so, under what conditions? If not, explain why not.
6. Suppose we have a relation schema R(A,B,C) representing a relationship between two entity sets with keys A and B, respectively, and suppose that R has (among others) the FDs A → B and B → A. Explain what such a pair of dependencies means (i.e., what they imply about the relationship that the relation models).