Consider the relation R = {A, B, C, D, E, F, G, H, I,J} and the set of functional dependencies F = { {A, B} -> {C}, {A} -> {D, E}, {B} -> {F}, {F} ->{G, H}, {D} -> {I, J} }.

(a) Proof {A}->{E,J} holds by using inference rules. (10 marks)

(b) Whether {A,B,C} is a super key? Whether {A,B,C} is a candidate key? Why? (10 marks)

(c) Whether {A,F} is a super key? Whether {A,F} is a candidate key? Why? (10 marks)

(d) Decompose R into 2NF. (10 marks)

(e) Decompose R into BCNF. (10 marks)