Bissoy.com
Doctors Medicines MCQs Q&A

Let R(A, B, C, D) be a relation schema and F = {A → BC, AB → D, B → C} be the set of functional dependencies defined over R. Which of the following represents the closure of the attribute set {B}?

Let R(A, B, C, D) be a relation schema and F = {A → BC, AB → D, B → C} be the set of functional dependencies defined over R. Which of the following represents the closure of the attribute set {B}? Correct Answer {B, C}

Concept:- 

Functional Dependencies:- Functional dependencies are the result of the interrelationship between attributes of any relation. Suppose in relation R, X and Y are two the two subsets of the set of attributes, Y is said to be functionally dependent on X if a given value of X uniquely determines the value of Y.

It is denoted by X → Y. It means Y depends upon X or X holds Y.

Here X is known as a determinant of functional dependency.

Explanation:-

Here, given R( A, B, C, D ) be a relation schema

and, F = {A → BC, AB → D, B → C} be the set of functional dependencies defined over R.

Closure of attributes {B}:-

B+ = { B }

     = { B , C } ( using B →C )

We can not determine any other attributes B and C  contained in the result set.

Thus, 

B+ = { B , C }

Related Questions

Consider the following four relational schemas. For each schema, all non-trivial functional dependencies are listed. The underlined attributes are the respective primary keys. Schema I: Field ‘courses’ is a set-valued attribute containing the set of courses a student has registered for. Non-trivial functional dependency: rollno → courses Schema II: Non-trivial functional dependencies: rollno, courseid → email email → rollno Schema III: Non-trivial functional dependencies: rollno, courseid → marks, grade marks → grade Schema IV: Non-trivial functional dependencies: rollno, courseid → credit courseid → credit Which one of the relational schemas above is in 3NF but not in BCNF?
For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct? 
The following functional dependencies hold true for the relational schema R{V, W, X, Y, Z}: V → W VW → X Y → VX Y → Z Which of the following is irreducible equivalent for this set of functional dependencies?
Relation R with an associated set of functional dependencies, F, is decomposed into BCNF. The redundancy (arising out of functional dependencies) in the resulting set of relations is
Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas Y and Z, where Y = (PR) and Z = (QRS). Consider the two statements given below. I. Both Y and Z are in BCNF II. Decomposition of X into Y and Z is dependency preserving and lossless Which of the above statements is/are correct?
The _______ is a set of all functional and multi values dependencies implied by a set of functional dependencies
A database of research articles in a journal uses the following schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE) The primary key is (VOLUME, NUMBER, STARTPAGE, ENDPAGE) and the following functional dependencies exist in the schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE) → TITLE (VOLUME, NUMBER) → YEAR (VOLUME, NUMBER, STARTPAGE, ENDPAGE) → PRICE The database is redesigned to use the following schemas. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE) (VOLUME, NUMBER, YEAR) Which is the weakest normal form that the new database satisfies, but the old one does not?  
A _________ Fc for F is a set of dependencies such that F logically implies all dependencies in Fc, and Fc logically implies all dependencies in F.
The algorithm that takes a set of dependencies and adds one schema at a time, instead of decomposing the initial schema repeatedly is
Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values. F = {CH → G, A → BC, B → CFH, E → A, F → EG} is a set of functional dependencies (FDs) so that F+ is exactly the set of FDs that hold for R. How many candidate keys does the relation R have?