Please answer questions 5-7, will rate. Thank you.

For this homework assignment, consider the schema R-(a..cD. and the following set Fof functional dependencies holds on R: A-, BC CDE 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, -(4,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 Problem 3. Compute (BCy Problem 4. Compute the canonical cover F Problem 5. Show that the decomposition of R into R : (4,B,C) and R,-(A,D,E) s not a dependency-preserving decomposition Problem 6. Give a lossless-join decomposition into BCNF of R Problem 7. Give a lossless-join, dependency preserving decomposition into 3NF of R