Consider the relation R = (A, B, C, D, E, F, G, H). Assume that the following set of FDs holds: F = {AB CEF GH, A D, F G, BF H, BCF ADE}.

1. List all the candidate keys of the relation R. Show your work.

2. Decompose the relation in the following normal forms (if it is not there already): a) 3NF, b) BCNF.

3. For each decomposition that you make, state if it is (i) lossless join and (ii) dependency preserving.