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Problem 1.[100 points total. Each has 20 points.] Consider the schema R (A, B, C, D, E, F) and the following set F of functional dependencies holds on R A BCD BC DE DA a. Compute A+ b. Prove that the decomposition R (A, B, C,F) and R2 (B, D, E, F) of R is a lossless-join decomposition. c. Give a BCNF decomposition of R using the functional dependencies in F d. Find the canonical cover Fc of F. e. Give a 3NF decomposition of R using the above canonical cover F