,3,4). Which of the following functional (-->) and multivalued  (-->>) dependencies can you infer does not hold over rela

Suppose you are given a relation R = (A,B,C,D,E) with the following functional dependencies: {CE -> D,D -> B,C -> A}. Identify the best normal form that R satisfies (1NF, 2NF, 3NF). Explain Why

3. Consider the relation schema R = (A,B,C,D). For each of the following set of FDs, do the following: (a) identify the candidate keys for R. (b) state whether or not the proposed decomposition of R is lossless join and dependency preserving. Justify your answers. 1. B→C, A→D; decompose into (B,C) and (A,D). 2. AB→D, D→A, D→C; decompose into (A,C,D) and (B,D). 3. A→BC, C→AD; decompose into ABC and AD. 4. A→B, B→C, C→D; decompose into AB and ACD. 5. A→B, BC, C→D; decompose into AB, AD and CD.

In the BCNF decomposition algorithm, suppose you use a functional dependency α → β to decompose a relation schema r(α, β, γ) into r1(α, β) and r2(α, γ). Give an example of an inconsistency that can arise due to an erroneousupdate, if the foreign-key constraint were not enforced on the decomposedrelations above.

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

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.

Consider the relation R(A,B,C,D,E,F,G) with the following functional dependencies: A-CDE, BF. Decompose the relation R to prevent the redundancy problems.

p.609, icon at Example 2 # 2. Let A be the set of all points in the plane with the origin removed. That is, Define a relation on A by the rule: A = {(x, y)|x, y = R} - {(0,0)}. (a, b)R(c, d) ↔ (a, b) and (c, d) lie on the same line through the origin. (a) Prove that R is an equivalence relation. (b) Describe the equivalence classes arising from the equivalence relation R in part (a). (c) If A is replaced by the entire plane, is R an equivalence relation?

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

Consider the relation R with the following functional dependencies: R(P,Q,R,D,E,F) FD = {P →Q,QR → D,E → R, D → P} Which of the following are the candidate keys? (a) PF, QF. (b) PF, QF, RF (c) PEF, QEF, DEF (d) PEF, QFR