Consider a relation R(A,B,C,D) Let the functional dependencies of R be

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Consider a relation R(A,B,C,D). Let the functional dependencies of R be

Problem 1
Consider a relation R(A,B,C,D). Let the functional dependencies of R be: AC->B,
B->A and D->C. Answer the following questions (show your work):
1. What are all the keys of R?
2. Find a minimal bases for the given functional dependencies (or prove the
given one is minimal)
3. Perform a (possibly non-dependency preserving) BCNF decomposition of
R
4. Use the 3NF synthesis algorithm to find a lossless-join dependency-preserving
decomposition of R into 3NF.
Problem 2
Consider a relation R(B,O,I,S,Q,D). Let the functional dependencies for R be:
I->O, S->D,I->B, IS->Q, B->O. Answer the same questions as Problem 1.