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

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.

The following digraph represents a relation R. a C b d List the ordered pairs in the relation. R = { }.

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.

1. A known relationship mode of R (U, F), U= (A, B, C, E, F, G, H, I, J, G); F={AB->E,ABE->FG, B->FI, C->J, CJ->I, G->H}; find the minimum cover of F, then use theNormal Form decomposition algorithm to decompose this mode to 3NF, and check if thedecomposition has the nonadditive join property.

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

Let X= {4,5,6}.If we define a relation R on X by (x,y)=R if x

1. Consider a relation schema R1(A, B, C, D) that satisfies the set of functional dependencies F1 ={A→B, B→C, C→A}.a) Calculate A + and (AC)+b) Can AB→ C? Justify your answer.c) Find all the candidate keys of R1 using F1 and show your steps to find them. 2. Consider a relation schema R2(A, B, C, D) that satisfies the set of functional dependencies F2 = {A→B, C→D, D→AC}.a) Is (AD) is candidate key of R2? Justify your answer.b) Is R2 in BCNF? Explain the reason to your answer.c) If R2 is not in BCNF, give a lossless-join BCNF decomposition of R2. Is this decomposition dependency preserving? 3. Consider a relation schema R3(A, B, C, D, E) that satisfies the set of functional dependencies F3 = {A → BC, AC → BD}.a) Calculate (AC)+ and (AE)+b) Is AB → C in F3 +? Justify your answer.c) Find the canonical cover Fc of F3.d) Is R3 in 3NF? Explain the reason to your answer. If R3 is not in 3NF, give a lossless-join, dependency preserving 3NF decomposition of R3.