1. Suppose there are a schema R=(A, B, C, D, E) and a set F of functional dependencies F = {A BC, CD E, B D, E A}. a) Show the decomposition of R into R(A, B, C) and R(A, D, E) is a lossless decomposition. b) Show the decomposition of R into R(A, B, C) and R(C, D, E) is not a lossless decomposition. Give a lossless decomposition into BCNF of R. Give a lossless, dependency preserving decomposition into 3NF of R.