1. Given R(A, B, C, D, E, F) and set of Functional Dependencies (FDs) F = {AB C,AD, ACD + E, C + F}, answer the following questions. (a) Find a (minimal) key for R. (b) Find a minimal cover for Ft. (C) Is R, F in Boyce-Codd Normal Form (BCNF)? If so, justify your answer. If not, decompose R and Ft until you obtain a set of BCNF schemas. Is your decomposition lossless? Is it dependency preserving? (d) Is R, F in Third Normal Form (3NF)? If so, justify your answer. If not, decom- pose R and Ft into a lossless, dependency preserving set of schemas. If such a decomposition does not exist, explain why