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Question 1 of 60 Quiz ID: q1

What is the primary problem with combining instructor and department information into a single relation as shown in the in_dep example?

Increased storage requirements due to repetition of information

Inability to represent null values for new departments without instructors

Violation of first normal form requirements

Both repetition of information and need for null values

Question 2 of 60 Quiz ID: q2

What characterizes a lossy decomposition in database design?

It eliminates all redundant data from the original relation

It cannot reconstruct the original relation from the decomposed relations

It violates all functional dependencies in the original schema

It requires more storage space than the original relation

Question 3 of 60 Quiz ID: q3

Which mathematical condition must hold for a decomposition to be lossless?

R₁ ∪ R₂ = R

Π_{R₁}(r) ⋈ Π_{R₂}(r) = r

R₁ ∩ R₂ = ∅

Π_{R₁}(r) × Π_{R₂}(r) = r

Question 4 of 60 Quiz ID: q4

What is the defining characteristic of first normal form (1NF)?

All attributes must have atomic domains

There should be no partial functional dependencies

All non-key attributes must depend on the full primary key

There should be no transitive dependencies

Question 5 of 60 Quiz ID: q5

Why is encoding information in application programs rather than the database considered a bad design practice?

It makes applications run slower

It violates the atomicity requirement of first normal form

It hides semantic constraints from the database system

It requires specialized programming languages

Question 6 of 60 Quiz ID: q6

What does the functional dependency α → β mean in terms of relation instances?

For every tuple, the value of α determines the value of β

Whenever two tuples agree on α, they must agree on β

α is a subset of β in every tuple

β is functionally dependent on α in at least one tuple

Question 7 of 60 Quiz ID: q7

What is the closure F⁺ of a set of functional dependencies F?

All functional dependencies that are explicitly stated in F

All functional dependencies that are trivial given F

All functional dependencies that are logically implied by F

All functional dependencies that violate BCNF

Question 8 of 60 Quiz ID: q8

How is a superkey defined using functional dependency notation?

K → R where K is a proper subset of R

K → R where K contains at least one non-prime attribute

K → R where K is a set of attributes

K → R (K determines all attributes of R)

Question 9 of 60 Quiz ID: q9

What distinguishes a candidate key from a superkey?

A candidate key must contain only prime attributes

A candidate key is a minimal superkey (no proper subset is a superkey)

A candidate key can have null values while a superkey cannot

A candidate key must be a single attribute

Question 10 of 60 Quiz ID: q10

When is a functional dependency considered trivial?

When it involves only key attributes

When it is satisfied by all instances of a relation

When the right-hand side is a subset of the left-hand side

When it can be inferred from other dependencies

Question 11 of 60 Quiz ID: q11

What are the two conditions that must be satisfied for a relation to be in Boyce-Codd Normal Form (BCNF)?

No partial dependencies and no transitive dependencies

All attributes must be atomic and all FDs must be trivial

For every FD α → β, either it is trivial or α is a superkey

For every FD α → β, β must contain only prime attributes

Question 12 of 60 Quiz ID: q12

How do you decompose a relation that violates BCNF due to a non-trivial dependency α → β where α is not a superkey?

Create relations (α ∪ β) and (R - α)

Create relations (α) and (β)

Create relations (α ∪ β) and (R - (β - α))

Create relations (α) and (R - β)

Question 13 of 60 Quiz ID: q13

What is dependency preservation in the context of database decomposition?

All functional dependencies must be preserved in at least one relation

All functional dependencies can be checked by examining individual relations

No functional dependencies are lost during decomposition

The decomposition must preserve all multivalued dependencies

Question 14 of 60 Quiz ID: q14

How does Third Normal Form (3NF) differ from BCNF?

3NF allows partial dependencies while BCNF does not

3NF is a stricter form of normalization than BCNF

3NF allows certain dependencies where the determinant is not a superkey

3NF requires all attributes to be prime

Question 15 of 60 Quiz ID: q15

What are the three goals of normalization?

Reduce storage, improve performance, eliminate redundancy

Each relation in good form, lossless decomposition, dependency preservation

Eliminate anomalies, ensure atomicity, preserve dependencies

Minimize joins, maximize indexing, ensure consistency

Question 16 of 60 Quiz ID: q16

Why might a relation in BCNF still have modification anomalies?

BCNF doesn't handle multivalued dependencies properly

BCNF allows partial functional dependencies

BCNF doesn't ensure atomic domains

BCNF doesn't eliminate transitive dependencies

Question 17 of 60 Quiz ID: q17

What are Armstrong's three axioms for functional dependencies?

Reflexivity, augmentation, transitivity

Reflexivity, union, decomposition

Augmentation, pseudotransitivity, union

Transitivity, decomposition, complementation

Question 18 of 60 Quiz ID: q18

What properties do Armstrong's axioms possess?

They are sound but not complete

They are complete but not sound

They are both sound and complete

They are neither sound nor complete

Question 19 of 60 Quiz ID: q19

Which rule can be derived from Armstrong's axioms?

If α → β and α → γ, then α → βγ (Union)

If α → β, then β → α (Commutativity)

If α → βγ, then α → β and α → β (Decomposition)

Both union and decomposition rules

Question 20 of 60 Quiz ID: q20

What is the purpose of computing the closure α⁺ of an attribute set α?

To find all attributes that are functionally determined by α

To identify the candidate keys of a relation

To determine if a relation is in BCNF

To compute the number of tuples in a relation

Question 21 of 60 Quiz ID: q21

How can attribute closure be used to test if α → β holds?

Check if α ⊆ β⁺

Check if β ⊆ α⁺

Check if α⁺ ∩ β⁺ ≠ ∅

Check if α⁺ = β⁺

Question 22 of 60 Quiz ID: q22

How can attribute closure be used to test if α is a superkey?

Check if α⁺ contains all attributes of R

Check if α⁺ contains at least one candidate key

Check if α⁺ = α

Check if α⁺ contains no redundant attributes

Question 23 of 60 Quiz ID: q23

What is a canonical cover of a set of functional dependencies?

A set that contains all possible FDs for a relation

A minimal set equivalent to the original with no redundancies

A set where all FDs have single attributes on the right side

A set that preserves all multivalued dependencies

Question 24 of 60 Quiz ID: q24

Which of the following demonstrates redundancy in a set of FDs?

{A → B, B → C, A → C} where A → C is redundant

{A → B, B → C, C → A} where all are necessary

{A → BC, B → D} where no redundancy exists

{AB → C, A → B} where both are necessary

Question 25 of 60 Quiz ID: q25

Given R = (A, B, C, D, E) and F = {A → BC, CD → E, B → D, E → A}, what is the closure of attribute set {A}?

{A, B, C}

{A, B, C, D}

{A, B, C, D, E}

{A, B, C, D, E, F}

Question 26 of 60 Quiz ID: q26

For the same R and F as above, is {A} a candidate key?

Yes, because A⁺ contains all attributes of R

No, because A doesn't determine all attributes directly

Yes, but only if no proper subset of A determines R

No, because E also determines A

Question 27 of 60 Quiz ID: q27

For the decomposition of R = (A, B, C, D, E) into R₁ = (A, B, C) and R₂ = (A, D, E), what is the common attribute set?

{A}

{A, B}

{C, D}

{B, E}

Question 28 of 60 Quiz ID: q28

Why is the decomposition into R₁ = (A, B, C) and R₂ = (A, D, E) lossless?

Because R₁ and R₂ have no common attributes

Because A → R₁ or A → R₂ holds

Because the common attribute A is a candidate key for R₁

Because all FDs are preserved in the decomposition

Question 29 of 60 Quiz ID: q29

What is the key difference between BCNF and 3NF in terms of the dependencies they allow?

BCNF allows partial dependencies while 3NF does not

3NF allows certain non-trivial FDs where the determinant is not a superkey

BCNF allows transitive dependencies while 3NF does not

3NF requires all attributes to be prime while BCNF does not

Question 30 of 60 Quiz ID: q30

Which normal form is primarily concerned with eliminating multivalued dependencies that are not functional dependencies?

Second Normal Form (2NF)

Boyce-Codd Normal Form (BCNF)

Fourth Normal Form (4NF)

Fifth Normal Form (5NF)

Question 31 of 60 Quiz ID: q31

In the context of normalization, what is a 'legal instance' of a relation?

An instance that satisfies all specified constraints

An instance that has no null values

An instance that is in first normal form

An instance that minimizes storage space

Question 32 of 60 Quiz ID: q32

What problem does the example with inst_info (ID, child_name, phone) illustrate?

The need for better indexing strategies

That BCNF doesn't address multivalued dependencies properly

The importance of choosing appropriate data types

That functional dependencies are insufficient for database design

Question 33 of 60 Quiz ID: q33

What is the pseudotransitivity rule derived from Armstrong's axioms?

If α → β and γ → δ, then αγ → βδ

If α → β and βγ → δ, then αγ → δ

If α → β and γβ → δ, then αγ → δ

If α → βγ, then α → β and α → γ

Question 34 of 60 Quiz ID: q34

Why is testing for superkey using attribute closure more efficient than checking all possible instances?

It requires examining only the schema, not the data

It works for any normal form, not just BCNF

It can be computed in polynomial time

It doesn't require knowledge of functional dependencies

Question 35 of 60 Quiz ID: q35

What is the time complexity of computing attribute closure α⁺ for a set of attributes?

O(1) constant time

O(n) linear in the number of attributes

O(n²) quadratic in the number of attributes

Exponential in the number of attributes

Question 36 of 60 Quiz ID: q36

In the decomposition process, why is dependency preservation desirable?

It ensures the decomposition is lossless

It allows efficient enforcement of constraints without joins

It guarantees the database will be in BCNF

It minimizes storage requirements

Question 37 of 60 Quiz ID: q37

What is the potential trade-off between BCNF and dependency preservation?

BCNF always guarantees dependency preservation

We can always achieve both BCNF and dependency preservation

Sometimes we must choose between BCNF and dependency preservation

Dependency preservation is more important than BCNF

Question 38 of 60 Quiz ID: q38

Which of the following is NOT a type of anomaly that normalization addresses?

Insertion anomalies

Deletion anomalies

Modification anomalies

Retrieval anomalies

Question 39 of 60 Quiz ID: q39

What does the union rule of functional dependencies state?

If α → β and α → γ, then α → βγ

If α → β and β → γ, then α → γ

If α → βγ, then α → β and α → γ

If α → β and γ → δ, then αγ → βδ

Question 40 of 60 Quiz ID: q40

What does the decomposition rule of functional dependencies state?

If α → β and α → γ, then α → βγ

If α → β and β → γ, then α → γ

If α → βγ, then α → β and α → γ

If α → β and γ → δ, then αγ → βδ

Question 41 of 60 Quiz ID: q41

In the context of functional dependencies, what does the term 'logically implied' mean?

The FD is explicitly stated in the set F

The FD must hold in every relation instance that satisfies F

The FD is trivial and therefore always holds

The FD is suggested by the attribute names but not necessarily true

Question 42 of 60 Quiz ID: q42

What is the minimality condition for a candidate key?

It must consist of the fewest possible attributes

No proper subset of it can be a superkey

It must contain at least one non-prime attribute

It must be a single attribute

Question 43 of 60 Quiz ID: q43

How does the concept of 'prime attribute' relate to normalization?

Prime attributes are those that appear in some candidate key

Prime attributes must be of integer type

Normalization seeks to eliminate all prime attributes

3NF requires that all attributes are prime

Question 44 of 60 Quiz ID: q44

What is the primary cause of repetition of information in the in_dep example?

The relation is not in first normal form

The relation contains a partial functional dependency

The relation contains a transitive dependency

Department information is repeated for each instructor

Question 45 of 60 Quiz ID: q45

Why is the decomposition of employee into employee1(ID, name) and employee2(name, street, city, salary) lossy?

Because it doesn't preserve all functional dependencies

Because we cannot reconstruct the original relation if two employees have the same name

Because it creates new insertion anomalies

Because it violates first normal form

Question 46 of 60 Quiz ID: q46

What is the fundamental insight behind the lossless join decomposition test?

The common attributes must form a superkey for at least one of the relations

The relations must have no common attributes

All functional dependencies must be preserved

The decomposition must be in BCNF

Question 47 of 60 Quiz ID: q47

In the attribute closure algorithm, what is the termination condition?

When result contains all attributes of R

When no new attributes can be added to result

When we have processed all functional dependencies once

When result becomes a superkey

Question 48 of 60 Quiz ID: q48

What is the significance of the example showing that Strings might not be atomic?

It demonstrates that 1NF is insufficient for good design

It shows that atomicity depends on how attributes are used

It proves that all databases should use only numeric types

It indicates that domain selection is irrelevant to normalization

Question 49 of 60 Quiz ID: q49

Why is the inst_info example used to motivate higher normal forms?

It shows that BCNF cannot eliminate all redundancy

It demonstrates that functional dependencies are insufficient

It illustrates the need for denormalization in practice

It proves that normalization is unnecessary

Question 50 of 60 Quiz ID: q50

What is the practical implication of the fact that Armstrong's axioms are sound and complete?

We can derive all possible FDs that hold using only these axioms

We need additional axioms to handle multivalued dependencies

The axioms only work for BCNF but not 3NF

The axioms are too complex for practical use

Question 51 of 60 Quiz ID: q51

In the context of FD theory, what does the term 'attribute set' refer to?

Any collection of attributes from a relation schema

Only sets that form candidate keys

Sets that appear on the left-hand side of FDs

Sets that contain only prime attributes

Question 52 of 60 Quiz ID: q52

What is the relationship between the closure of attribute sets and the closure of functional dependencies?

They are the same concept with different names

Attribute closure can be used to compute FD closure

FD closure is a superset of attribute closure

They are unrelated concepts in database theory

Question 53 of 60 Quiz ID: q53

Why is the concept of 'canonical cover' important in database design?

It minimizes the number of FDs that need to be checked

It guarantees that the database will be in BCNF

It ensures all FDs have single attributes on the right side

It eliminates the need for normalization

Question 54 of 60 Quiz ID: q54

What is the potential problem with having redundant functional dependencies?

They consume extra storage space

They can lead to inconsistent constraint enforcement

They violate the atomicity requirement of 1NF

They prevent the database from being in BCNF

Question 55 of 60 Quiz ID: q55

In the decomposition process, what is the significance of identifying that a relation is not in 'good form'?

It indicates the relation should be deleted entirely

It suggests the relation should be decomposed

It means the relation contains too many attributes

It shows that the relation has too many tuples

Question 56 of 60 Quiz ID: q56

What is the role of functional dependencies in the definition of normal forms?

They are irrelevant to normal forms

They provide the formal criteria for evaluating normal forms

They are only used in 1NF but not higher normal forms

They are replaced by multivalued dependencies in higher normal forms

Question 57 of 60 Quiz ID: q57

How does the concept of 'lossless join' relate to the practical use of databases?

It ensures that queries return correct results after decomposition

It guarantees that all queries will run faster

It eliminates the need for backup and recovery

It makes the database immune to hardware failures

Question 58 of 60 Quiz ID: q58

What is the practical significance of the fact that not all decompositions are good?

It shows that decomposition should be avoided entirely

It emphasizes the need for careful database design

It proves that normalization theory is flawed

It suggests that all databases should use a single table

Question 59 of 60 Quiz ID: q59

Why is the ability to test functional dependencies using attribute closure important?

It allows efficient constraint checking during database design

It eliminates the need for database administrators

It makes all databases automatically normalized

It ensures that all queries are optimized

Question 60 of 60 Quiz ID: q60

What is the fundamental trade-off in database normalization?

Between storage efficiency and query performance

Between data redundancy and constraint enforcement complexity

Between normalization level and application simplicity

Between elimination of anomalies and preservation of dependencies

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