Consider the following database schema: R(A, B, C, D, E, F, G) with the set of functional dependencies

{A E, AD BE, AC E, E B, BG F, BE D, BDH E, F A, D H, CD A}

3.1 Find the candidate keys of this schema.

3.2 Find a 3NF decomposition of this schema (list both the relations and the corresponding set of functional dependencies). Show the details of your work.

3.3 Find a BCNF decomposition of this schema (list both the relations and the corresponding set of functional dependencies). Show the details of your work.