1. Prove that IR2 of the Armstrong Inference Rules is correct (sound). We did that for IR3 in class. Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) for the next 6 questions. 2. Use all three of Armstrong Rules to "infer" one new FD. 3. Find a minimal cover for F. 4. Find all many keys for R. 5. Find a 3NF decomposition for R that is dependency preserving and has lossless join. 6. Find a BCNF decomposition for R that has lossless join. 7. Apply the lossless join test algorithm on the decomposition of Q6 or the decomposition of Q7 to verify that the decomposition is a lossless join decomposition. You do not need to do that for both Q6 and Q7.

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