For this homework assignment, consider the schema R (A,B,C,D,E) and the following set F of functional dependencies holds on R: E A B D CD E A BC

Problem 1. Suppose that we decompose the schema R into ( , , ) R1 A B C and ( , , ) R2 A D E . Show that this decomposition is a lossless-join decomposition with respect to F .

Problem 2. Suppose that we decompose the relation schema R into ( , , ) R3 A B C and ( , , ) R4 C D E . Show that this decomposition is not a lossless-join decomposition.

Hint: Give an example of a relation r on schema R such that ,,() ,,()

Problem 3. Compute ( ) . BC

Problem 4. Compute the canonical cover . FC

Problem 5. Show that the decomposition of R into ( , , ) R1 A B C and ( , , ) R2 A D E is not a dependency-preserving decomposition.

Problem 6. Give a lossless-join decomposition into BCNF of R .

Problem 7. Give a lossless-join, dependency preserving decomposition into 3NF of R .