Use the chase test to tell whether each of the following dependencies hold in a relation R(A, B, C, D, E) with the dependencies A →→ BC, B → D, and C →→ E. a)A → D. b) A →→ D. c)A → E. d)A →→ E. Please answer all of them with explanations. Thanks

Consider a relation T with seven attributes ABCDEFG where AB is a composite primary key for T. Assume T has the following functional dependencies: AB -> CDEFG L A-> CEF F-> E In what normal form is relation T? Explain why? I Is it possible to decompose T into a number of relations in order to achieve a higher normal form? Explain how and show tables. 券

Consider the relation instance and functional dependencies below. Which of these FDs hold on the instance and which do not? A BC 2 4 АВ — С A → B A → C В > с АС — В ВС — А 3 4 В > А C → A C → B 1 3 5 2 4

Solve the following:

Let W(A, B) and Q(C,D) be two relation schemas. Let r₁ and r2 be the corresponding relation instances. B is a foreign key that refers to C in r2. Assuming that all tuples in r₁ and r2 satisfy referential integrity constraints, which of the following is ALWAYS TRUE? (А) Пв (г1) - Пс (rz) =Ø (B) IIc (₂)-118 (1₁) = 0 (С) Пв (г1 ) = Пс (12) (D) Пв (r1 ) - Пс (12) +Ø OB OD OA O C

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

Consider the relation R = {A, B, C, D, E, F, G, H, I,J} and the set of functional dependencies F = { {A, B} → {C}, {A} → {D, E}, {B} → {F}, {F} →{G, H}, {D} → {I, J} }. (b) Whether (A,B,F} is a super key? Whether {A,B,F} is a candidate key? Why? (c) Whether {A,D} is a super key? Whether {A,D} is a candidate key? Why?

For each of the following pairs of expressions, give instances of relations thatshow the expressions are not equivalent. ΠA(r − s) and ΠA(r) − ΠA(s).

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Consider the relation R(A,B,C,D,E), with A as a key. We also have the functional dependency CEA. Can redundancies occur in R ? Explain.