1Which of the following data integrity rules states that no primary key attribute may be NULL?
A.Referential Integrity
B.Entity Integrity
C.Domain Integrity
D.Key Integrity
Correct Answer: Entity Integrity
Explanation:The Entity Integrity rule states that no primary key value can be NULL because the primary key is used to uniquely identify individual tuples in a relation.
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2In the context of Relational Database Design, what does the notation represent?
A.Multivalued Dependency
B.Transitive Dependency
C.Functional Dependency
D.Join Dependency
Correct Answer: Functional Dependency
Explanation:The notation represents a Functional Dependency, indicating that the value of attribute set is determined uniquely by the value of attribute set .
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3Which specific anomaly occurs when valid data cannot be recorded in the database because the primary key for that record is not yet available?
A.Update Anomaly
B.Deletion Anomaly
C.Insertion Anomaly
D.Modification Anomaly
Correct Answer: Insertion Anomaly
Explanation:An Insertion Anomaly occurs when certain attributes cannot be inserted into the database without the presence of other attributes, specifically the primary key.
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4A relation is said to be in First Normal Form (1NF) if and only if:
A.All attributes share a single primary key
B.There are no transitive dependencies
C.Every attribute contains only atomic (indivisible) values
D.There are no partial dependencies
Correct Answer: Every attribute contains only atomic (indivisible) values
Explanation:1NF prohibits repeating groups and requires that the domain of each attribute contains only atomic values.
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5Given a relation schema with the Functional Dependency set . Which axiom allows us to infer ?
A.Reflexivity Rule
B.Augmentation Rule
C.Transitivity Rule
D.Union Rule
Correct Answer: Transitivity Rule
Explanation:Armstrong's Transitivity Rule states that if and , then .
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6Which Normal Form eliminates Partial Functional Dependencies?
A.First Normal Form (1NF)
B.Second Normal Form (2NF)
C.Third Normal Form (3NF)
D.Boyce-Codd Normal Form (BCNF)
Correct Answer: Second Normal Form (2NF)
Explanation:A relation is in 2NF if it is in 1NF and no non-prime attribute is dependent on any proper subset of any candidate key (elimination of partial dependency).
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7Consider a relation where is the primary key. If there exists a dependency , which normal form is violated?
A.1NF
B.2NF
C.3NF
D.BCNF
Correct Answer: 2NF
Explanation:Since is the primary key, is a proper subset of the key. The dependency is a Partial Dependency, which violates 2NF.
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8A functional dependency is considered trivial if:
A.
B.
C.
D. is a candidate key
Correct Answer:
Explanation:A trivial functional dependency is one that is always satisfied, which occurs when the right-hand side () is a subset of the left-hand side ().
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9Which of the following conditions must be met for a relation to be in Third Normal Form (3NF)?
A.It must be in BCNF
B.It must be in 2NF and contain no multivalued dependencies
C.It must be in 2NF and contain no transitive dependencies
D.It must allow repeating groups but no partial dependencies
Correct Answer: It must be in 2NF and contain no transitive dependencies
Explanation:3NF requires the relation to be in 2NF and that no non-prime attribute is transitively dependent on the primary key.
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10In the context of 3NF, for a functional dependency (where is not in ) to be valid, which condition is sufficient?
A. is a prime attribute (part of a candidate key)
B. is a proper subset of a candidate key
C. is a composite attribute
D. is a non-prime attribute
Correct Answer: is a prime attribute (part of a candidate key)
Explanation:For 3NF, for every non-trivial FD , either must be a superkey OR must be a prime attribute.
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11Boyce-Codd Normal Form (BCNF) is considered stricter than 3NF because:
A.It does not allow multivalued dependencies
B.It requires every determinant to be a candidate key
C.It prohibits the right-hand side of a dependency from being a prime attribute
D.It requires relations to be in 4NF first
Correct Answer: It requires every determinant to be a candidate key
Explanation:BCNF removes the allowance in 3NF where the right-hand side of a dependency is a prime attribute. In BCNF, for every non-trivial dependency , must be a superkey.
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12Identify the scenario where 3NF allows a dependency but BCNF does not.
A.A non-prime attribute determining another non-prime attribute
B.A proper subset of a candidate key determining a non-prime attribute
C.A non-key attribute determining a part of a candidate key
D.A candidate key determining a non-prime attribute
Correct Answer: A non-key attribute determining a part of a candidate key
Explanation:If a non-key attribute determines a part of a composite candidate key (and the determinant is not a superkey), 3NF allows it (because the RHS is prime), but BCNF prohibits it.
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13Which symbol is used to denote a Multivalued Dependency?
A.
B.
C.
D.
Correct Answer:
Explanation:The double-headed arrow is the standard notation for Multivalued Dependencies (e.g., ).
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14Fourth Normal Form (4NF) deals specifically with the elimination of:
Explanation:A relation is in 4NF if it is in BCNF and contains no non-trivial multivalued dependencies.
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15If a relation scheme is decomposed into and , the decomposition is said to be lossless if:
A.
B.
C. or
D. contains the same number of tuples as
Correct Answer: or
Explanation:For a lossless join decomposition, the common attributes () must be a superkey for at least one of the decomposed relations ( or ).
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16Referential integrity constraints are primarily used to maintain consistency between:
A.Two distinct databases
B.Two tables in a relationship
C.Two columns in the same table
D.The database and the application layer
Correct Answer: Two tables in a relationship
Explanation:Referential integrity ensures that a Foreign Key in one table points to a valid Primary Key in another table, maintaining the relationship consistency.
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17Which of the following is true regarding Armstrong's Axiom of Reflexivity?
A.If , then
B.If , then
C.If and , then
D.If , then
Correct Answer: If , then
Explanation:Reflexivity states that if a set of attributes is a subset of , then functionally determines .
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18What is the closure of a set of attributes (denoted as )?
A.The set of all candidate keys in the relation
B.The set of all attributes that are functionally determined by
C.The set of all attributes that determine
D.The set of attributes required to normalize the relation
Correct Answer: The set of all attributes that are functionally determined by
Explanation:The closure includes itself and all attributes that can be inferred to be dependent on using the set of functional dependencies.
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19Consider relation with FDs: . What is the closure of ?
A.
B.
C.
D.
Correct Answer:
Explanation: gives . gives . gives . Starting with , we get . Thus, all attributes are included.
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20Which normal form protects against data inconsistency caused by Update Anomalies?
A.Only 1NF
B.Normalization in general (2NF, 3NF, etc.)
C.Unnormalized forms
D.Denormalization
Correct Answer: Normalization in general (2NF, 3NF, etc.)
Explanation:The primary goal of normalization (moving through 1NF, 2NF, 3NF, etc.) is to reduce redundancy, which directly prevents update anomalies where data might become inconsistent if updated in one place but not another.
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21A table is considered to be in BCNF if:
A.It is in 2NF and has no transitive dependencies
B.For every functional dependency , is a superkey
C.It has no composite primary keys
D.It is in 3NF and has no multivalued dependencies
Correct Answer: For every functional dependency , is a superkey
Explanation:This is the formal definition of BCNF. It ensures no attribute is determined by anything other than a superkey.
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22What defines a Multivalued Dependency in a relation ?
A.For a value of , there is a specific single value of
B.For a value of , there is a set of values for , and this set is dependent on
C.For a value of , there is a set of values for , and this set is independent of
D. determines and determines
Correct Answer: For a value of , there is a set of values for , and this set is independent of
Explanation:An MVD exists when determines a set of values for , and that set is solely determined by , regardless of the values of other attributes () in the relation.
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23If a relation has only two attributes, it is always in at least which Normal Form?
A.2NF
B.3NF
C.BCNF
D.4NF
Correct Answer: BCNF
Explanation:In a binary relation , the only possible dependencies are trivial, (A is key), (B is key), or both. In all valid non-trivial cases, the determinant is a superkey, satisfying BCNF.
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24Which of the following statements about Prime Attributes is true?
A.They are attributes that are not part of any candidate key
B.They are attributes that contain NULL values
C.They are attributes that are a member of some candidate key
D.They are always integer types
Correct Answer: They are attributes that are a member of some candidate key
Explanation:A prime attribute is defined as an attribute that appears in at least one candidate key of the relation.
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25Consider the relation with and . This relation violates 3NF because of:
A.Partial dependency
B.Transitive dependency
C.Multivalued dependency
D.Cyclic dependency
Correct Answer: Transitive dependency
Explanation: exists via . Since determines but is not a candidate key (assuming A is key), is transitively dependent on .
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26The process of decomposing a relation with a Multivalued Dependency into two relations usually results in schemas:
A. and
B. and
C. and
D. and
Correct Answer: and
Explanation:To resolve the MVD in relation , we decompose it into and to satisfy 4NF.
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27Which rule allows us to combine and into ?
A.Decomposition Rule
B.Union Rule
C.Pseudo-transitivity Rule
D.Reflexivity Rule
Correct Answer: Union Rule
Explanation:The Union rule of Armstrong's axioms states that if determines and determines , then determines both and together.
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28A functional dependency is a full functional dependency if:
A.Removal of any attribute from means the dependency no longer holds
B.Removal of any attribute from means the dependency no longer holds
C. and are composite attributes
D. is the primary key
Correct Answer: Removal of any attribute from means the dependency no longer holds
Explanation:Full functional dependency means is dependent on the whole of , not just a subset of .
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29Which of the following implies that a relation is definitely in 1NF?
A.The relation has a composite primary key
B.The relation has no foreign keys
C.The intersection of any two rows is empty
D.All underlying domains contain atomic values only
Correct Answer: All underlying domains contain atomic values only
Explanation:The fundamental requirement of 1NF is the atomicity of attribute values.
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30If a relation is in BCNF, it is also automatically in:
A.4NF
B.5NF
C.3NF
D.DKNF
Correct Answer: 3NF
Explanation:Normalization is hierarchical. BCNF is a stronger form of 3NF. Therefore, if a relation is in BCNF, it satisfies all conditions for 3NF, 2NF, and 1NF.
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31What is the primary purpose of Domain Integrity constraints?
A.To ensure rows are unique
B.To ensure data values fall within a defined valid range or set
C.To link tables together
D.To prevent hardware failures
Correct Answer: To ensure data values fall within a defined valid range or set
Explanation:Domain integrity restricts the values that can be stored in a column to a specific format, range, or set of allowed values (e.g., Age > 0).
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32Consider with Key . Which dependency represents a Partial Dependency?
A.
B.
C.
D.
Correct Answer:
Explanation:The candidate key is composite . The dependency relies on only a part of the key (), making it a partial dependency.
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33Armstrong's Axioms are said to be sound and complete. What does 'complete' mean?
A.The rules contain no errors
B.They can generate all implied functional dependencies from a set
C.They apply to all databases
D.They automatically normalize the database
Correct Answer: They can generate all implied functional dependencies from a set
Explanation:Completeness means that the axioms allow us to derive every valid functional dependency that is logically implied by the initial set.
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34Given . What is the Pseudo-transitivity rule application if we also know ?
A.
B.
C.
D.
Correct Answer:
Explanation:Pseudo-transitivity states: If and , then . Here, applying it to and , we get .
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35A relation schema is in 4NF if it is in BCNF and:
A.Every join dependency is trivial
B.Every multivalued dependency is a functional dependency
C.For every non-trivial MVD , is a superkey
D.It contains no composite keys
Correct Answer: For every non-trivial MVD , is a superkey
Explanation:4NF restricts Multivalued Dependencies. If a non-trivial MVD exists, the determinant must be a superkey.
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36Which of the following is NOT an Armstrong Axiom?
A.Reflexivity
B.Augmentation
C.Transitivity
D.Commutativity
Correct Answer: Commutativity
Explanation:The three primary Armstrong Axioms are Reflexivity, Augmentation, and Transitivity. Commutativity is not one of them.
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37When converting a 1NF relation to 2NF, what is the primary action taken?
A.Remove columns with NULL values
B.Remove subsets of data that apply to multiple rows and place them in separate tables
C.Create separate tables for sets of values that apply to a part of the primary key
D.Combine tables to reduce joins
Correct Answer: Create separate tables for sets of values that apply to a part of the primary key
Explanation:2NF involves removing partial dependencies by moving attributes dependent on only part of a composite key to a new relation.
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38In a relation , if and are independent multivalued attributes, meaning and , which normal form is violated if all are in one table?
A.2NF
B.3NF
C.BCNF
D.4NF
Correct Answer: 4NF
Explanation:This describes a scenario where determines a set of s and a set of s independently. Storing them in one table creates a Cartesian product redundancy, violating 4NF.
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39Which axiom states: If , then ?
A.Reflexivity
B.Augmentation
C.Transitivity
D.Composition
Correct Answer: Augmentation
Explanation:Augmentation allows adding attributes to both sides of a functional dependency.
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40If an attribute is a determinant in a dependency , it means:
A. determines the value of
B. determines the value of
C. and are logically unrelated
D. is a Foreign Key
Correct Answer: determines the value of
Explanation:In , the attribute on the left side () is called the determinant.
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41Why is the dependency preserving property desirable in decomposition?
A.It reduces storage space
B.It ensures constraints can be checked without joining relations
C.It ensures the original relation can be reconstructed
D.It eliminates all null values
Correct Answer: It ensures constraints can be checked without joining relations
Explanation:If a decomposition preserves dependencies, the DBMS can enforce validity constraints by checking the individual decomposed tables rather than performing expensive joins.
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42Which of the following is true about a trivial Multivalued Dependency ?
A. is the entire relation schema
B.
C.Both A and B
D.Neither A nor B
Correct Answer: Both A and B
Explanation:An MVD is trivial if or if forms the entire relation schema.
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43What is a 'Superkey'?
A.A minimal set of attributes that uniquely identifies a tuple
B.Any set of attributes that uniquely identifies a tuple
C.A foreign key that references a primary key
D.A key used for encryption
Correct Answer: Any set of attributes that uniquely identifies a tuple
Explanation:A superkey is any set of attributes that ensures uniqueness. A Candidate Key is a minimal Superkey.
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44Data Integrity Rules are generally enforced by:
A.The Operating System
B.The Database Management System (DBMS)
C.The End User
D.The Network Layer
Correct Answer: The Database Management System (DBMS)
Explanation:The DBMS is responsible for monitoring and enforcing integrity constraints (entity, referential, domain) during data modification.
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45Consider . Functional Dependencies: and . The key is . Is this in BCNF?
A.Yes, because determinants are superkeys
B.No, because holds and Instructor is not a superkey
C.Yes, because all attributes are prime
D.No, because of multivalued dependency
Correct Answer: No, because holds and Instructor is not a superkey
Explanation:While it is in 3NF (since Course is a prime attribute), it is not in BCNF because the determinant 'Instructor' is not a superkey for the whole relation.
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46Redundancy in a database often leads to:
A.Faster query processing
B.Reduced storage costs
C.Data inconsistencies
D.Higher security
Correct Answer: Data inconsistencies
Explanation:Storing the same data in multiple places (redundancy) makes it difficult to keep all copies synchronized during updates, leading to inconsistency.
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47Which operation is used to compute the closure of a set of functional dependencies ?
Explanation:The closure of a set of dependencies is found by applying Armstrong's inference rules (Axioms) until no new dependencies can be derived.
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48In the Decomposition Rule: If , then:
A. and
B. and
C.
D. only
Correct Answer: and
Explanation:The decomposition rule allows breaking down the right-hand side of a functional dependency.
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49A Candidate Key is:
A.A Superkey with no proper subset that is also a Superkey
B.Any set of attributes with the Unique constraint
C.The primary key chosen by the database administrator
D.A key that allows NULL values
Correct Answer: A Superkey with no proper subset that is also a Superkey
Explanation:This defines the 'minimality' property of a candidate key.
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50If a relation is in 3NF but not BCNF, what specific structure must exist?
A.A non-trivial MVD
B.Two overlapping candidate keys
C.A partial dependency
D.All attributes must be non-prime
Correct Answer: Two overlapping candidate keys
Explanation:The difference between 3NF and BCNF usually arises when there are multiple candidate keys that overlap (share a common attribute), and a dependency exists where a non-key attribute determines a part of a key.