Functional Dependencies and Normalization · Database Management System · GATE CSE

Let $P, Q, R$ and $S$ be the attributes of a relation in a relational schema. Let $X \rightarrow Y$ indicate functional dependency in the context of a relational database, where $X, Y \subseteq\{P, Q, R, S\}$ Which of the following options is/are always true?

In the context of relational database normalization, which of the following statements is/ are true?

Which of the following statements about a relation $R$ in first normal form (1NF) is/are TRUE?

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 superkeys in the relation R is _________.

Consider the following statements S1 and S2 about the relational data model:

S1: A relation scheme can have at most one foreign key.

S2: A foreign key in a relation scheme R cannot be used to refer to tuples of R.

Which one of the following choices is correct? 

(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, YEAR, PRICE)

(VOLUME, NUMBER, STARTPAGE, ENDPAGE) → TITLE
(VOLUME, NUMBER) → YEAR
(VOLUME, NUMBER, STARTPAGE, ENDPAGE) → PRICE

(VOLUME, NUMBER, STARTPAGE, ENDPAGE, TITLE, PRICE)
(VOLUME, NUMBER, YEAR)

In the context of schema normalization in relational DBMS, consider a set $F$ of functional dependencies. The set of all functional dependencies implied by $F$ is called the closure of $F$. To compute the closure of $F$, Armstrong's Axioms can be applied. Consider $X, Y$, and $Z$ as sets of attributes over a relational schema. The three rules of Armstrong's Axioms are described as follows.

Reflexivity: If $Y \subseteq X$, then $X \rightarrow Y$

Augmentation: If $X \rightarrow Y$, then $X Z \rightarrow Y Z$ for any $Z$

Transitivity: If $X \rightarrow Y$ and $Y \rightarrow Z$, then $X \rightarrow Z$

The additional rule of Union is defined as follows.

Union: If $X \rightarrow Y$ and $X \rightarrow Z$, then $X \rightarrow Y Z$

It can be proved that the additional rule of Union is also implied by the three rules of Armstrong's Axioms. Listed below are four combinations of these three rules. Which one of these combinations is both necessary and sufficient for the proof?

Consider the following relational schema along with all the functional dependencies that hold on them.

$$\begin{aligned} & R 1(A, B, C, D, E):\{D \rightarrow E, E A \rightarrow B, E B \rightarrow C\} \\ & R 2(A, B, C, D):\{A \rightarrow D, A \rightarrow B, C \rightarrow A\} \end{aligned}$$

Which of the following statement(s) is/are TRUE?

Consider a relational schema team(name, city, owner), with functional dependencies \{name $\rightarrow$ city, name $\rightarrow$ owner}.

The relation team is decomposed into two relations, $t 1$ (name, city) and $t 2$ (name, owner). Which of the following statement(s) is/are TRUE?

A functional dependency $F: X \to Y$ is termed as a useful functional dependency if and only if it satisfies all the following three conditions:

• $X$ is not the empty set.
• $Y$ is not the empty set.
• Intersection of $X$ and $Y$ is the empty set.

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

Suppose the following functional dependencies hold on a relation U with attributes P, Q, R, S, and T :

P → QR

RS → T

Which of the following functional dependencies can be inferred from the above functional dependencies?  

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

Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D₁ : R = [(P, Q, S, T); (P, T, X); (Q, Y); (Y, Z, W)]

D₂ : R = [(P, Q, S); (T, X); (Q, Y); (Y, Z, W)]

Which one of the following options is correct?

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 : n (1 on the side of E₁ and n on the side of E₃) relationship R₁₃.

E₁ has two single-valued attributes a₁₁ and a₁₂ of which a₁₁ is the key attribute. E₂ has two single-valued attributes a₂₁ and a₂₂ of which a₂₁ is the key attribute. E₃ has two single-valued attributes a₃₁ and a₃₂ of which a₃₁ is the key attribute. The relationships do not have any attributes.

If a relational model is derived from the above ER model, then the minimum number of relations that would be generated if all the relations are in 3NF is _______.

Which one of the following is CORRECT?

How many candidate keys does the relation $$R$$ have?

The relation $$R$$ is

Assume { Author, Title } is the key for both schemes. Which of the following statements is true?

A disk seek takes $$4ms$$, disk data transfer bandwidth is $$300MB/s$$ and checking a tuple to see if amount is greater than $$x$$ takes $$10\mu s.$$ Which of the following statements is correct?

Which one of the following options is false?

Which of the following functional dependencies is NOT implied by the above set?

Name, courseNo $$\,\, \to \,\,$$ grade
RollNo, courseNo $$\,\, \to \,\,$$ grade
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,$$ Name $$\,\, \to \,\,$$ rollNo
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,$$ RollNo $$\,\, \to \,\,$$ name

The highest normal form of this relation scheme is

The relation (Roll_number, Name, Date_of_Birth, Age) is

Which of the following functional dependencies are satisfied by the instance?

(b) Suppose the attributes Book–title and Author–address are added to the relation, and the primary key is changed to {Name–of–Author, Book–title}, what will be the highest normal form satisfied by the relation?

(b) Suppose the attributes Book–title and Author–address are added to the relation, and the primary key is changed to {Name–of–Author, Book–title}, what will be the highest normal form satisfied by the relation?

Which of the following statements is true about the referential integrity constraint above?

(b) Determine the minimal keys of relation $$R.$$