Normalization Here is a set of FDs for a relation R {A, B, C, D, E, F, G}; AB BC>DE AEF>G AC>DE a. Compute the closure of {A, C}, i.e. (A, C}* b. What are the candidate keys for R? Justify your answer. c. Is R in BCNF? Justify your answer. d. Give a 3NF decomposition of this relation.

2.Consider relation R=(A,B,C,D) with the following FDs: B → C, C > D, and D A a. List all candidate keys of R. b. Is R in 3NF? BCNF? Justify your answer

21. of 40 A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if every decomposed relation is in BCNF. Let R(A,B,C,D,E,F,G) be a relation with the functional dependencies: C→ E, EG→ D, DG-→A, and A→ BF. If we decompose R into relations R1(C, D, G), R2(A, D, G), R3(A, B, F), and R4(C, E), which of the following statements is TRUE? Select one: O The decomposition is in BCNF but Not in 3NF. The decomposition is in 3NF and in BCNF. The decomposition is in 3NF but Not in BCNF. O The decomposition is Not in 3NF and Not in BCNF.

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…