Exercise 1
Consider a relation with schema R (A, B, C, D) and FDs the set F:
F= {
AB→C
C→D
D→A }
• (10%) Find all the candidate keys of R.
• (5%) Indicate all BCNF violations for R.
• (10%) Decompose the relations into collections of relations that are in BCNF.
• (5%) Indicate which dependencies, if any, are not preserved by the BCNF decomposition.
Exercise 2
Consider a relation with schema R (A, B, C, D) and FDs the set F:
F ={ A→B
A→C
C→D }
• (5%) Determine the set of all candidate keys for the relation schema.
• (5%) Determine the highest normal form (no NF, 1NF, 2NF, 3NF, BCNF) that the relation
schema is in. Explain your answer.
• (10%) Decompose the relation schema into new relation schemas that satisfy the next higher
normal form.
• (10%) Show the minimal covers of functional dependencies for the decomposed relation
schemas.
• (10%) List the candidate keys of the decomposed relation schemas.
• (10%) Prove that the decomposition is a lossless join decomposition and/or dependency
preserving.