Compute the closure of the following set F of functional dependencies for relation schema R = (A, B, C, D, E). A → BC CD → E B → D E → A List the candidate keys for R.

Give all the keys of R if the functional dependencies on R in each of the following cases

Implement in Python / Java Algorithm: Testing for lossless (nonadditive) join property. Input: A universal relation R, a decomposition D = { R1, R2, R3, ….. Rm } of R, and a set F of functional dependencies. 1. Create an initial matrix S with one row i for each relation in Ri in D, and one column j for each attribute Aj in R. 2. Set S(i, j) := bij for all matrix entries. (* each bij is a distinct symbol associated with indices (i, j) * ) {for each column j representing attribute Aj                                  {if (relation Ri includes attribute Aj ) then set S(I, j):=aj;};};             (* each aj is a distinct symbol associated with index (j) *)   3. For each row i representing relation schema Ri {for each functional dependency X  → Y in F            {for all rows in S which have the same symbols in the columns               corresponding to attributes in X                  {make the symbols in each column that correspond to                                 an attribute in Y be…

Let R be the relation on the set {a,b,c,d} containing the ordered pairs (a,a), (a,c), (b,b), (b,c), (b,d), (c,b), (c,c), (d,a) and (d,d). Find R².

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

Give a BCNF decomposition to relation "r" according to the given functional dependencies. Show the steps of normalization clearly to get full credit. r(U, V, W, X, Y, Z) Z-> XY X -> VW V-> U XY -> Y

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