g set of five functional dependencies which hold on R: A → B A C BD → E EC → A E →G ompute the closure of each of the following ur sets of attributes with respect to F:CE,7 BCD and ADE
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- Show that the following decomposition of the schema R of Exercise 7.1 is not alossless decomposition:(A, B, C)(C, D, E).Hint: Give an example of a relation r(R) such that ΠA, B, C (r) ⋈ ΠC, D, E (r) ≠ rConsider a relation schema R(A, B, C, D, E, G) and a set of functional dependencies F = {A → C, AD → CE, B → ACD, C → B}. (a) Show the steps of computing a canonical cover for F. (b) Compute the closure of AG and then determine whether or not AG is a candidate key. (c) Determine whether or not (A, E, G) is in BCNF and justify your answer using the transitive closure of a set of attributes. If (A, E, G) is not in BCNF, find a BCNF decomposition of it. (d) Assume that (A, E, G) is decomposed into (A, G) and (E, G). Given the above functional dependencies, is this decomposition always lossless? If so, prove this. Otherwise, explain it using an example (i.e., a case of decomposing a table containg rows and columns into two tables). (e) Assume that R is decomposed into R1(A, B, C, D) and R2(A, E, G). Is this decomposition dependency preserving? Justify your answer.Consider a relation schema R(A,B,C,D,E,H,G) F = {A->BC, B->C, C->BED, BD-> E, E->D, AG->E, G->H, AH->G} 3NF decomposition of r
- Consider a relation schema R = {A, B, C, D, E} and its functional dependency set F = {A → BC,CD → E,B →D,E → A}. Let R be decomposed into R1 and R2, where R1 = (A,B,C) and R2 = (A,D,E). Is the decompositionlossless? Is the decomposition dependency preserving? (a) The decomposition is lossless and dependency preserving.(b) The decomposition is neither lossless nor dependency preserving.(c) The decomposition is not lossless but dependency preserving.(d) The decomposition is lossless but not dependency preserving.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 aboveConsider the relation schema R(A, B, C, D, E, F) and the set S = {AB->C, BC->AD, D->E, C->B) of functional dependencies. Assuming that R is decomposed into the relation schemas R1(A,B), R2(B,C), R3(A,B,D,E) and R4(E,F). Use the Chase test to show if this is a lossless decomposition.
- Consider the relation schema R (A, B, C, D, E, F, G, H) with the set of functional dependencies K = {A→B, B→DE, F→H, G→CE}. Determine all candidate keys of R in a systematic manner (do not use the Armstrong's Axioms) and explain how you determine them. Show each step.Consider the relation schema R (A, B, C, D) with all possible functional dependencies. For each of the following situations, identify the highest normal form for this relation R. A, C -> B, D C -> D A, C -> B, D B -> D A, C -> B, DConsider 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.
- Consider a relation with schema R(A,B,C,D,E,G) and functional dependencies (FDs) C→D; B→A; D→E; E→G ) What is the closure of {B,C}? Show steps of your solution. Find 2 nontrivial FDs that can be inferred from the given FDs set. Explain how you found them. Propose one key for a given schema and FDs. Explain how you found it.Consider a relation R(A,B,C,D,E) with functional dependencies AB→C, A→D, and D→E. (a) What are the keys for R?(b)What is the closure A, that is A+ ? What is the closure AB, that is (AC)+ ?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