Show that it is possible to ensure that a dependency-preserving decomposition into 3NF is a lossless decomposition by guaranteeing that at least one schema contains a candidate key for the schema being decomposed. (Hint: Show that the join of all the projections onto the schemas of the decomposition cannot have more tuples than the original relation.)

Q: Let X = {0, 1}. (a) List (as subsets of X X X) all possible relations on X. This answer has not been…

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Q: Consider the schema R = (A, B, C, D, E, G) and the set F of functional depen- dencies: AB → CD ADE…

A: a. To find the candidate keys of R, we need to determine the attribute closure of every subset of…

Q: Consider a relation with schema R(A,B,C,D,E,G) and functional dependencies (FDs) C→D; B→A; D→E; E→G…

A: Answer is given below .

Q: Consider the relation R(S, N, R, C, J, H, L) and its set of dependencies F = {S, N -> C ; J, H, C ->…

A: using Armstrong's axioms=> proved in figure figure 1:

Q: Consider relations R(A, B, C), S(C, D, E) and T(E, F, G). Find a re- lational expression which (1)…

A: The expression first applies the selection σ(​B<D) to R and S, which eliminates all rows from R…

Q: Find a minimal cover in a standard form for the relation schema R(A, B,C, D, E, F, G, H) with the…

A: A minimal cover or canonical cover means a minimum set of functional dependencies. A canonical cover…

Q: Assume you apply a functional dependence in the BCNF decomposition technique to deconstruct a…

A: Intro Assume you apply a functional dependence in the BCNF decomposition technique to deconstruct a…

Q: SIf a decomposition of a relation R into R¡ and R2 is lossless, then which of the followings are…

A: If a decomposition of a relation “R” into “R1”, and “R2” is lossless then it produces “R” by…

Q: Consider the schema R=ABCDEG and the set of functional dependencies F={BC→AG, BG→CD, C→AE, D→AG} 2a)…

A: To address each part of your question:2a) Determine the keys of the schema:To find the keys of the…

Q: 1. If we project the relation R(A,B,C,D,E) with dependencies A→→BC, B→D, and C→→E onto S(A,C,E),…

A: Answer is given below-

Q: Decompose R into a set of 3NF relations, that is lossless join and dependency preserving.

A: Here we decompose it in 3nf and check dependency preserving.…

Q: Comment say : True / False. whether the decomposition of R ( A, B, C,D , E , G) in (ABCE , BD , AEG…

A: Introduction : Given , Relational Schema R(A,B,C,D,E,G).And its functional dependencies are also…

Q: Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) 5. Find a 3NF…

A: The given Functional depenency are :  F = {BC -> D, B -> E, CE -> D, E -> CA, BF ->…

Q: Minimization of a logical function with Weich maps:  Vm(0,1,2,3,4,5,6,7,10,13)

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Q: Consider the following set F of functional dependencies on the relation schema R = (A, B, C, D, E,…

A: a) Candidate Key : Minimal set of attributes used to differentiate every record of the table is…

Q: Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) 8.Apply the lossless…

A: Decomposition of a relation is done when a relation in relational model is not in appropriate normal…

Q: Let S = {1,2,3}. Let be the relation on S x S defined by (a, b) ≤ (c,d) a ≤ c and b>d (a) Show that…

A:

Q: Define a relation R on Z×Z by (m,n)R(s,t) if and only if m-n = s-t. Is R reflexive? symmetric?…

A: In the given case, we prove all three one by one.

Q: Let S = {1,2,3}. Let be the relation on Sx S defined by (a, b) ≤ (c,d) a ≤ c and b>d (a) Show that…

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Q: R = ABCD F3{C-D, C-А, В -С } A. Find all candidate keys. B. What is the strongest normal form that…

A: A) Attribute or set of attribute that can determine all the attribute of relation R is key of R.…

Q: The division operator of relational algebra, “÷”, is defined as follows. Let r(R)and s(S) be…

A: Given: The division operator of relational algebra, “÷”, is defined as follows. Let r(R)and s(S) be…

Q: aniversity consists of several dep nesters. Students take admission urer (any lecturer may take dif…

A: In the above question, given is the table schedule for each session and venue. We are required to…

Q: Decompose the relations, as necessary, into collections of relations that are in BCNF. R(A,B,C,D)…

A:

Q: Explain aproximiation and how it can be achieved by fuzzy relation with simple example

A: Answer: A connection is a mathematical representation of a situation in which certain elements of a…

Q: -------If R is reflexive, symmetric and transitive then the relation is said to be Floor(2.4) +…

A:

Q: 3. Suppose you are given a relation R(PQRSM)and the F, the set of functional dependencies that hold…

A: R(P, Q, R, S, M)  PQ -> R PQ -> S R -> P S->Q (PQ) + ={PQRS} (RS) + ={RSPQ} Therefore…

Q: A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if…

A: I have provided solution in step2

Q: Is it feasible to have two clustering indices for distinct search keys on the same relation in…

A: A connection to data with a specific value is provided by an index. Indices help you find what…

Q: Consider the relation R on Z? given by: R= {((a,b), (c, d)) : a + d = c+ b} Prove that R is an…

A: Z denotes set of all integers {....,-3,-2,-1,0,1,2,...} i.e, both positive and negative. So, Z2…

Q: Let R(A, B, C) be arelational schema with the following functional dependencies : {A— >B,B—>C,C— >A}…

A: To determine whether the decomposition of R into (A, B) and (B, C) satisfies the properties of…

Q: A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if…

A: ANSWER IS C   R is not IN 3NF and not in BCNF

Q: {1,2,3,4} . Find the symmetric and reflexive closures of R.

A: Given relation R R={(1,2),(1,4),(2,3),(3,1),(4,2)} We have to find symmetric and reflexive closure…

Q: Compute a canonical cover Fc of F = { A → E, BC → D, C → A, AB → D, D → G, BC → E, D → E, BC → A },…

A: Answer: We need to explain the how to find the canonical cover Fc in the given relation. so we will…