For this homework assignment, consider the schema R=(A,B,C,D,E) and the following set F of functional dependencies holds on R: A BC CD E BD EA Problem 1. Suppose that we decompose the schema R into R=(A,B,C) and R. =(A,D,E). Show that this decomposition is a lossless-join decomposition with respect to F. Problem 2. Suppose that we decompose the relation schema R into R = (A,B,C) and R=(C,D,E). Show that this decomposition is not a lossless-join decomposition. Hint: Give an example of a relation r on schema R such that r # IIA,B,C(r) ~ IIc,d,e(r) Problem 3. Compute (BC)