GATE CSE
Database Management System
Functional Dependencies and Normalization
Previous Years Questions

## Marks 1

In a relational data model, which one of the following statements is TRUE?
Consider a relation R(A, B, C, D, E) with the following three functional dependencies. AB $$\to$$ C ; BC $$\to$$ D ; C $$\to$$ E; The number of superk...
A database of research articles in a journal uses the following schema. (VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE) The primary key is (V...
Consider the relation $$X\left( {P,Q,R,S,T,U} \right)$$ with the following set of functional dependencies \eqalign{ & F = \left\{ \, \right.... The maximum number of superkeys for the relation schemaR(E, F, G, H)$$with$$E$$as key is ______. A prime attribute of a relation scheme$$R$$is an attribute that appears Consider the relation schema$$R = \left( {E,\,F,\,G,\,H,\,I,\,J,\,K,L,\,M,\,N} \right)$$and the set of functional dependencies$$\left\{ {\left\{ {E...
Which of the following is TRUE?
Which one of the following statements about normal forms is FALSE?
A table has fields, $$F1, F2, F3, F4, F5,$$ with the following functional dependencies: $$F1 \to F3.\,F2 \to F4.\,\,\,\left( {F1\,.\,F2} \right) \to ... Relation$$R$$with an associated set of functional dependencies,$$F,$$is decomposed into$$BCNF.$$The redundancy (arising out of functional depend... Consider a schema$$R(A,B,C,D)$$and functional dependencies$$A \to B\,\,$$and$$C \to D\,\,$$. Then the decomposition of$$R$$into$${R_1}\left( {...
Let $$R=(A,B,C,D,E,F)$$ be a relation scheme with the following dependencies: $$C \to F,\,E \to A,\,EC \to D,\,A \to B.$$ Which of the following is a ...
Which normal form is considered adequate for normal relational database design?
State True or False with reason. There is always a decomposition into Boyce-codd normal form $$(BCNF)$$ that is lossless and dependency preserving.

## Marks 2

Consider the relation R(P, Q, S, T, X, Y, Z, W) with the following functional dependencies. PQ → X; P → YX; Q → Y; Y → ZW Consid...
Consider a relational table R that is in 3NF, but not in BCNF. Which one of the following statements is TRUE?
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...
Consider an Entity-Relationship (ER) model in which entity sets E1 and E2 are connected by an m : n relationship R12. E1 and E3 are connected by a 1 :...
Given the following two statements: $$S1:$$ Every table with two single-valued attributes is in $$1NF, 2NF, 3NF$$ and $$BCNF.$$ $$S2:$$ $$AB \to C,\,\... Relation$$R$$has eight attribution$$ABCDEFGH.$$Fields of$$R$$contain only atomic values.$$F = \left\{ {CH \to G,\,\,A \to BC,\,B \to CFH,\,\,E ...
Relation $$R$$ has eight attribution $$ABCDEFGH.$$ Fields of $$R$$ contain only atomic values. $$F = \left\{ {CH \to G,\,\,A \to BC,\,B \to CFH,\,\,E ... Consider the following relational schemes for a library database. Book ( Title, Author, Catalog_ no, Publisher, Year, Pr ice ) Collection ( Title, Aut... Let$$R\left( {A,B,C,D} \right)$$be a relational schema with the following functional dependencies:$$A \to B,\,\,B \to C,\,\,C \to D$$and$$D \to ...
Let $$R\left( {A,\,B,\,C,\,D,E,P,G} \right)$$ be a relational schema in which the following functional dependencies are known to hold: $$AB \to CD,\,... Which one of the following statements if FALSE? Consider the relation enrolled (student, course) in which (student, course ) is the primary key, and the relation Paid (student, amount) where student... The following functional dependencies are given :$$\eqalign{ & AB \to CD,\,AF \to D,\,\,DE \to F, \cr & C \to G.\,\,\,\,\,\,\,\,\,\,F \...
In a schema with attributes $$A, B, C, D,$$ and $$E,$$ following set of functional dependencies are given \eqalign{ & \,\,\,A \to B \cr &... Consider a relation schemeR = \left( {A,\,B,\,C,\,D,\,E,\,H} \right)$$on which the following functional dependencies hold:$$\left\{ {A \to B,\,\,...
The relation scheme student Performance (Name, CourseNo, RollNo, Grade) has the following functional dependencies: Name, courseNo $$\,\, \to \,\,$$ gr...
A relation Empdt $$1$$ is defined with attributes empcode (unique), name, street, city, state and pincode. For any pincode, there is only one city and...
Consider the following functional dependencies in a database. \eqalign{ & \,\,\,\,Date\,\,of\,\,Birth\,\, \to \,\,Age \cr & \,\,\,\,\,... From the following instance of a relation schemaR(A, B, C),$$we can conclude that: ... Relation$$R$$is decomposed using a set of functional dependencies,$$F,$$and relation$$S$$is decomposed using another set of functional dependenc...$$R(A,B,C,D)$$is a relation. Which of the following does not have a lossless-join, dependency preserving$$BCNF$$decomposition? Given the following relation instance$$\eqalign{ & X\,\,\,\,\,Y\,\,\,\,\,Z \cr & \,\,1\,\,\,\,\,\,4\,\,\,\,\,\,2 \cr & \,\,1\,\...
Consider the schema $$R = \left( {S\,\,T\,\,U\,\,V} \right)$$ and the dependencies $$S \to T,\,\,T \to U,\,\,U \to V$$ and $$V \to S$$ let $$R =$$ $$(... Consider the following database relations containing the attributes Book–id Subject–Category–of–book Name–of–Author Nationality–of–Author With book–id... Consider the following database relations containing the attributes Book–id Subject–Category–of–book Name–of–Author Nationality–of–Author With book–id... Let$$R (a, b, c)$$and$$S(d, e, f)$$be two relations in which$$d$$is the foreign key of$$S$$that refers to the primary key of$$R.$$Consider t... For a database relation$$R(a,b,c,d),$$where the domains of$$a, b, c, d$$include only atomic values, only the following functional dependencies and... (a) Consider the relation scheme$$R(A, B, C)$$with the following functional dependencies:$$\eqalign{ & A,B \to C \cr & \,\,\,\,\,\,C ...
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