This is an individual (not a team) assignment.

Turn in your answers to these problems on paper.

1. Consider a relation R with five attributes ABCDE. You are given the following dependencies: A -> B, BC -> E, and ED -> A.

• (a) What are all of the candidate keys in R?
• (b) Is R in 3NF?
• (c) Is R in BCNF?

2. Suppose that you are given a relation R with four attributes ABCD. For the functional dependencies in parts (a) and (b) below...

• identify the candidate key(s) for R
• indicate whether or not R is in BCNF
• indicate whether or not it is in 3NF
• if R is not in BCNF, provide a lossless decomposition such that the new relations are in BCNF

(a) C -> D, C -> A, B -> C

(b) B -> C, D -> A