Consider a relation schema R = {A, B, C, D, E} and its functional dependency set F = {A → B,CD → E,B →D,E → A}. Compute A+ and choose the answer. (a) A+ = AB (b) A+ = ABC (c) A+ = ABCD (d) A+= ABCDE (e) none of the above

QUESTION 6 Consider the following functional dependencies for a relation R(A, B, C, D) A -> (B, C, D), (A, D) -> (B, C) (C, D) -> (A, B) Identify the candidate key(s). O {C, D} O {A}, {C, D}, {A, D} O {A}, {C,D} O A

Consider the universal relation: R = (A, B, C, D, E, F, G, H, I, J) and the set of functional dependencies:  A, B -> C  B, D -> E, F  A, D -> G, H  A -> I  H -> J What is the key for R? And Decompose R into 2NF, and then into 3NF relations.

Let A1, A2, and A3 be attributes in a relation R. If both of these functional dependencies hold: A1 → A2 and A2 → A3, then A1 → A3 holds, because of the_? rule.

Consider a relational schema R = {A, B, C, D, E, G, H}, satisfying the functional dependencies F = {E → G, E → H, G → H, A → BC, BC → D, C → H, EG → A}. a) Derive all candidate keys for this schema. b) Derive a canonical cover of the functional dependencies in F. c) Is the above schema in BCNF? Prove or disprove. If it is not in BCNF, convert it into BCNF. d) Is the BCNF schema from (c) dependency-preserving? Prove or disprove. If not, convert into 3NF.

Consider the relation schema Appointment={Patient, GP, Date, Time, Clinic, Room} and the followingset Σ of FDs:• Patient, Clinic, Date → Time• Patient → GP• GP → Clinic• Clinic, Date, Time, Room → Patient• Patient, Date, Time → Clinic, RoomIs the above relation schema Appointment in BCNF? If not, identify a BCNF decomposition for Appointment. You need to include the main steps used for identifying the BCNF decomposition. Check ifthis BCNF decomposition is dependency preserving

Calculate the following transitive closures

You are given a relation R with the following attributes R(A,B,C,D,E). Assume that you were given the following functional dependencies: • FD1= AB -> E • FD2: = D -> C (a) What is a valid key for this relation? justify your response. (b) Is this relation in 3NF (Third Normal Form)? Justify your response. If it is not in 3NF, normalize the relation and demonstrate all steps of normalization.

Answer the given question with a proper explanation and step-by-step solution.

39 of 40 Let R = (A, B, C, D) be a relation schema with the FD's: A → B and B → A. R has how many superkeys? (Write your answer as an integer). write your answer here