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 R(ABCDEFG) be a relation and F={A -> C, A-> D, B->F, E->F, F->G} a. Show example of lossless…

A: According to the information given:- We have R(ABCDEFG) F={A -> C, A-> D, B->F, E->F,…

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

A:

Q: Suppose ρ is the relation defined on P({1, 2, 3}) in which, for A, B ∈ P({1, 2, 3}), AρB means "A…

A: Given: P({1, 2, 3}) A, B ∈ P({1, 2, 3}) AρB means "A and B both have exactly 2 elements."  ρ is…

Q: Which of the followings can possibly be a canonical cover Fc of a set F of functional dependencies?…

A: The answer to this question is option b) {A → D, AB → C, D → B} and d) {A → C, D → B, AB → C}

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 set of F of the following functional dependencies on relation R(A, B, C, D, E): AB C…

A:

Q: Consider the relation R = {A, B, C, D, E, F, G, H, I,J} and the set of functional dependencies F = {…

A: f ={     AB → C,      A → D,      B → F,  F → GH,  D → IJ   } To find the key check the RHS of the…

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: The relation R(A, B, C, D, E) has the following functional dependencies. А, В - С В, С -> D C, D→E…

A: Attached Solution for (a) and (b) part:

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: Consider a relation R(A,B,C,D,E) with functional dependencies AB→C, A→D, and D→E. (a) What are…

A: (A ) keys for relation R) is AB   Reason : -- because key is column or set of columns using that you…

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: ind a minimal covering of these functional dependencies. Then use it to synthesize a set of…

A:

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: Consider a relation R={A,B,C,D,E,F,G,H,I} with the set of functional dependencies and determine,…

A: Now we must determine the above definition whether for each FD. Each value is super key or not on…

Q: Given a relation schema R = (A, B, C) and its functional dependencies F = {A →B, B→ C). Suppose R is…

A: Answer is given below-

Q: From the given set of functional dependencies,determine that there can be more than one canonical…

A: Functional dependency is a relationship that is shown between two or more attributes of a table.…

Q: Consider a schema R and a set F of functional dependencies as follows: R= (A,B,C,D,E,G). F = {A →…

A: First of  all , let’s understand what is super key.      Super key : Super key can be defined as  an…

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: Consider a schema R and a set F of functional dependencies as follows: R = (A,B,C,D,E). F = {A →…

A: To check for lossless join decomposition using functional dependency, the following set of the…

Q: Consider the relation R = {F, T, D, N, S} and the set of functional dependencies K = {F¬D, {D, T}…

A:

Q: Given 5 dimensional parameters A, B, C, D, E, F and the following set S of functional dependencies S…

A: The set of functional dependencies are given as follows-  S={B→A;C→B;F→E;B→F;F→D};   Let us find the…