1Which data integrity rule states that no part of a primary key can be null?
data integrity rules
Easy
A.Entity integrity
B.Referential integrity
C.Domain integrity
D.User-defined integrity
Correct Answer: Entity integrity
Explanation:
Entity integrity ensures that every row has a unique, non-null primary key so that each record can be uniquely identified.
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2Which rule ensures that a foreign key value must match an existing primary key value in the referenced table, or be null?
data integrity rules
Easy
A.Column integrity
B.Referential integrity
C.Domain integrity
D.Entity integrity
Correct Answer: Referential integrity
Explanation:
Referential integrity maintains consistency between two tables by ensuring that foreign key values always point to valid, existing primary key values.
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3In the context of relational databases, what does the notation represent?
functional dependency
Easy
A. is equal to
B. is a subset of
C. functionally determines
D. functionally determines
Correct Answer: functionally determines
Explanation:
The notation means that the attribute functionally determines the attribute , meaning each value of is associated with exactly one value of .
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4A functional dependency is considered trivial if:
functional dependency
Easy
A. and are disjoint
B. is a subset of
C. is a subset of
D. is a primary key
Correct Answer: is a subset of
Explanation:
A functional dependency is trivial if the right-hand side is a subset of the left-hand side (e.g., ).
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5According to Armstrong's axioms, if and , then . What is this rule called?
functional dependency
Easy
A.Union rule
B.Augmentation rule
C.Reflexivity rule
D.Transitivity rule
Correct Answer: Transitivity rule
Explanation:
The transitivity rule states that if attribute determines , and determines , then determines .
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6What is the primary objective of database normalization?
need of normalization
Easy
A.To combine all tables into one large table
B.To increase data redundancy
C.To minimize data redundancy and avoid anomalies
D.To speed up data retrieval by avoiding joins
Correct Answer: To minimize data redundancy and avoid anomalies
Explanation:
Normalization is the process of organizing data to reduce redundancy and eliminate unwanted insert, update, and delete anomalies.
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7Which of the following occurs when deleting a row in a table unintentionally causes the loss of other independent data?
need of normalization
Easy
A.Insertion anomaly
B.Update anomaly
C.Deletion anomaly
D.Redundancy anomaly
Correct Answer: Deletion anomaly
Explanation:
A deletion anomaly happens when deleting a record representing one fact inadvertently deletes data representing another distinct fact.
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8A relation is in First Normal Form (1NF) if every attribute contains:
first normal form
Easy
A.Only atomic (indivisible) values
B.Repeating groups
C.Composite values
D.Transitive dependencies
Correct Answer: Only atomic (indivisible) values
Explanation:
First Normal Form (1NF) dictates that a domain is atomic if its elements are considered to be indivisible units. There can be no multivalued attributes or repeating groups.
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9Which of the following is explicitly forbidden in First Normal Form (1NF)?
first normal form
Easy
A.Null values
B.Primary keys
C.Foreign keys
D.Repeating groups or arrays
Correct Answer: Repeating groups or arrays
Explanation:
1NF requires that each column contains only a single value per row, strictly forbidding arrays, lists, or repeating groups of data.
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10For a table to be in Second Normal Form (2NF), it must first be in 1NF and free of:
second normal form
Easy
A.Transitive dependencies
B.Partial dependencies
C.Multivalued dependencies
D.Functional dependencies
Correct Answer: Partial dependencies
Explanation:
2NF requires that every non-prime attribute is fully functionally dependent on the entire primary key, meaning there are no partial dependencies.
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11When does a partial dependency occur?
second normal form
Easy
A.When a non-prime attribute depends on only a part of a composite primary key
B.When a non-prime attribute depends on a non-prime attribute
C.When a prime attribute depends on a non-prime attribute
D.When a table has no primary key
Correct Answer: When a non-prime attribute depends on only a part of a composite primary key
Explanation:
A partial dependency exists when an attribute that is not part of the primary key is dependent on only a portion of a composite primary key.
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12A table is in Third Normal Form (3NF) if it is in 2NF and has no:
third normal form
Easy
A.Partial dependencies
B.Primary keys
C.Atomic values
D.Transitive dependencies
Correct Answer: Transitive dependencies
Explanation:
3NF eliminates transitive dependencies, meaning non-prime attributes cannot depend on other non-prime attributes.
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13In 3NF, for every non-trivial functional dependency , which of the following must be true?
third normal form
Easy
A. is a superkey OR is a prime attribute
B. is a subset of
C. is a prime attribute AND is a superkey
D. is a foreign key
Correct Answer: is a superkey OR is a prime attribute
Explanation:
The strict definition of 3NF allows a dependency if is a superkey or if is part of a candidate key (a prime attribute).
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14Boyce-Codd Normal Form (BCNF) is widely considered to be a stronger version of which normal form?
boyce codd normal form
Easy
A.3NF
B.2NF
C.1NF
D.4NF
Correct Answer: 3NF
Explanation:
BCNF is a stricter extension of 3NF. A table in BCNF is always in 3NF, but a table in 3NF is not necessarily in BCNF.
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15For a relation to be in BCNF, for every non-trivial functional dependency , what must be?
boyce codd normal form
Easy
A.A superkey
B.A foreign key
C.A composite attribute
D.A prime attribute
Correct Answer: A superkey
Explanation:
In BCNF, the only condition allowed for a non-trivial functional dependency is that the determinant () must be a candidate key or superkey.
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16Which normal form removes the 3NF allowance that the dependent attribute can be a prime attribute when the determinant is not a candidate key?
boyce codd normal form
Easy
A.1NF
B.2NF
C.BCNF
D.4NF
Correct Answer: BCNF
Explanation:
BCNF drops the 3NF exception that allows to be a prime attribute when is not a superkey, making it stricter.
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17Which symbol is used to denote a multivalued dependency between attributes and ?
multivalued dependencies
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The double arrow notation () is used to signify a multivalued dependency.
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18A multivalued dependency occurs when there are at least how many attributes in a relation?
multivalued dependencies
Easy
A.Three
B.It depends on the primary key size
C.One
D.Two
Correct Answer: Three
Explanation:
Multivalued dependencies require at least three attributes (e.g., A, B, and C) where A determines multiple values of B and C independently of each other.
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19A table is in Fourth Normal Form (4NF) if it is in BCNF and contains no:
fourth normal form
Easy
A.Functional dependencies
B.Transitive dependencies
C.Partial dependencies
D.Multivalued dependencies
Correct Answer: Multivalued dependencies
Explanation:
Fourth Normal Form (4NF) specifically deals with the elimination of non-trivial multivalued dependencies in a table.
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20If a relation has two independent multivalued attributes (e.g., an employee's skills and their hobbies), putting them in the same table usually violates which normal form?
fourth normal form
Easy
A.3NF
B.4NF
C.1NF
D.2NF
Correct Answer: 4NF
Explanation:
Combining independent multivalued attributes creates a multivalued dependency, which violates 4NF.
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21Which data integrity rule is violated if a foreign key in a child table references a primary key value in a parent table that does not exist?
data integrity rules
Medium
A.Entity Integrity Rule
B.Key Integrity Rule
C.Domain Integrity Rule
D.Referential Integrity Rule
Correct Answer: Referential Integrity Rule
Explanation:
The Referential Integrity Rule states that every foreign key value must either be null or match an existing primary key value in the referenced table. A mismatch indicates a violation.
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22According to the Entity Integrity Rule, why must a primary key attribute never contain a NULL value?
data integrity rules
Medium
A.Because a primary key is used to uniquely identify individual tuples, and NULL implies an unknown or unassigned identity.
B.Because NULL values consume too much storage space in the database block.
C.Because indexing structures like B-Trees crash when encountering NULL primary keys.
D.Because foreign keys cannot reference composite primary keys if any part is NULL.
Correct Answer: Because a primary key is used to uniquely identify individual tuples, and NULL implies an unknown or unassigned identity.
Explanation:
Entity integrity ensures that every row can be uniquely identified. Since NULL represents an unknown value, allowing NULL in a primary key would prevent accurate identification of that specific record.
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23Given a relation and the functional dependencies and , which of Armstrong's axioms logically implies that ?
functional dependency
Medium
A.Augmentation Rule
B.Decomposition Rule
C.Transitivity Rule
D.Reflexivity Rule
Correct Answer: Transitivity Rule
Explanation:
Armstrong's Transitivity Rule states that if and hold true, then also holds true. Here, and implies .
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24If a functional dependency is considered 'trivial', what must be the relationship between sets of attributes and ?
functional dependency
Medium
A. and together form a superkey
B. is a subset of
C. is a proper subset of
D. and have no attributes in common
Correct Answer: is a subset of
Explanation:
A functional dependency is trivial if is a subset of . For example, is trivial because determining from is inherently true.
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25Suppose holds in a relation . According to the Augmentation Rule, what additional functional dependency is guaranteed to hold for any attribute ?
functional dependency
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The Augmentation Rule states that if , then for any set of attributes . Applying this to with attribute gives .
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26In an unnormalized database, updating a student's address might require changing multiple rows if the student is enrolled in multiple courses. What type of problem is this?
need of normalization
Medium
A.Insertion anomaly
B.Referential anomaly
C.Deletion anomaly
D.Update anomaly
Correct Answer: Update anomaly
Explanation:
An update anomaly occurs when data redundancy requires the same piece of information (like a student's address) to be updated in multiple places. If one instance is missed, the database becomes inconsistent.
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27Which of the following best describes a 'deletion anomaly' in a relational database?
need of normalization
Medium
A.Being unable to add a new record because it lacks a primary key value.
B.The unintentional loss of data about one entity when deleting a record about another entity.
C.A failure that occurs when attempting to delete a primary key referenced by a foreign key.
D.Data inconsistencies resulting from partially completed transaction rollbacks.
Correct Answer: The unintentional loss of data about one entity when deleting a record about another entity.
Explanation:
A deletion anomaly happens when deleting a row to remove facts about one entity inadvertently destroys the only record containing facts about a completely different entity.
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28A relation has an attribute Skills that contains values like 'Java, Python, SQL' in a single tuple. To bring into First Normal Form (1NF), what must the designer do?
first normal form
Medium
A.Remove all transitive dependencies from the relation.
B.Create a new primary key that includes the Skills attribute.
C.Ensure all non-key attributes are dependent on the primary key.
D.Modify the schema so that every attribute contains only atomic (indivisible) values.
Correct Answer: Modify the schema so that every attribute contains only atomic (indivisible) values.
Explanation:
1NF strictly dictates that every attribute must hold single, atomic values. Comma-separated lists violate 1NF and must be resolved by creating separate rows or tables.
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29Which of the following conditions is a strict requirement for a table to be in First Normal Form (1NF)?
first normal form
Medium
A.All columns must have unique names and hold values of the same domain.
B.Every non-prime attribute must depend on the whole primary key.
C.There must be no partial functional dependencies.
D.There must be no composite candidate keys.
Correct Answer: All columns must have unique names and hold values of the same domain.
Explanation:
Along with atomicity, 1NF requires that columns have unique names, the order of columns/rows does not matter, and values in a column belong to the same domain.
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30A relation has a composite primary key . A functional dependency exists. Which normal form is violated by this relation?
second normal form
Medium
A.3NF
B.BCNF
C.2NF
D.1NF
Correct Answer: 2NF
Explanation:
2NF requires that there be no partial dependencies. Since depends only on (which is a part of the composite primary key ), this is a partial dependency, violating 2NF.
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31If a relation has a single-attribute primary key and is already in 1NF, what can be immediately concluded about its 2NF status?
second normal form
Medium
A.It is in 2NF only if there are no transitive dependencies.
B.It is automatically in 2NF because partial dependencies are impossible.
C.It requires a check for multivalued dependencies to confirm 2NF status.
D.It automatically violates 2NF and must be decomposed.
Correct Answer: It is automatically in 2NF because partial dependencies are impossible.
Explanation:
A partial dependency means a non-prime attribute depends on part of a composite primary key. If the primary key is a single attribute, it cannot be partitioned, meaning partial dependencies cannot exist.
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32A relation has primary key . The dependencies are and . To normalize this to 3NF, how should the relation be decomposed?
third normal form
Medium
A. and
B. and
C.No decomposition is needed; it is already in 3NF.
D. and
Correct Answer: and
Explanation:
The dependency is a transitive dependency ( depends on the non-prime attribute ). To remove it and achieve 3NF, we place in its own relation, and leave in the parent relation.
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33According to the formal definition of 3NF, for every non-trivial functional dependency , either must be a superkey, OR which of the following must be true?
third normal form
Medium
A. must be a prime attribute (part of a candidate key).
B. and must be disjoint sets.
C. must be functionally dependent on a non-prime attribute.
D. must be a single attribute.
Correct Answer: must be a prime attribute (part of a candidate key).
Explanation:
In 3NF, a functional dependency is allowed if is a superkey OR if is a prime attribute. If neither condition holds, it constitutes a transitive dependency violation.
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34A table Orders has attributes OrderID, CustomerID, and CustomerName. The functional dependencies are OrderIDCustomerID, CustomerName and CustomerIDCustomerName. What anomaly is most likely if this remains unnormalized?
third normal form
Medium
A.Updating a customer's name requires changing multiple order records.
B.Querying the customer's name will return multiple different strings.
C.Deleting an order prevents the addition of new customers.
D.Inserting a new order will accidentally delete customer information.
Correct Answer: Updating a customer's name requires changing multiple order records.
Explanation:
Because CustomerName depends transitively on OrderID via CustomerID, a single customer placing multiple orders will have their name duplicated. Updating the name means updating all those order records (update anomaly).
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35What is the defining rule that distinguishes Boyce-Codd Normal Form (BCNF) from Third Normal Form (3NF)?
B.BCNF eliminates multivalued dependencies, which 3NF ignores.
C.BCNF requires all attributes to be atomic.
D.BCNF does not allow the right side of a dependency to be a prime attribute unless the left side is a superkey.
Correct Answer: BCNF does not allow the right side of a dependency to be a prime attribute unless the left side is a superkey.
Explanation:
3NF allows if is a prime attribute, even if is not a superkey. BCNF is stricter and removes this exception; MUST be a superkey for every non-trivial dependency.
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36Under which specific condition is a relation guaranteed to be in BCNF if it is already in 3NF?
boyce codd normal form
Medium
A.If the relation has overlapping candidate keys.
B.If the relation has at least three attributes.
C.If the relation has only one candidate key.
D.If the relation contains no composite keys.
Correct Answer: If the relation has only one candidate key.
Explanation:
A relation in 3NF can only violate BCNF if there are multiple overlapping candidate keys. If there is only a single candidate key, any 3NF relation is automatically in BCNF.
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37In a relation , a multivalued dependency exists. What does this imply about the relationship between attributes and ?
multivalued dependencies
Medium
A. and are entirely independent of one another, but both are determined by .
B. is a subset of .
C. functionally determines .
D. and must together form a candidate key.
Correct Answer: and are entirely independent of one another, but both are determined by .
Explanation:
A multivalued dependency occurs when two or more independent multivalued facts about the same attribute () are stored in the same table, making and independent of each other.
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38Suppose a Professor teaches multiple Courses and enjoys multiple Hobbies. If Courses and Hobbies are independent, representing this in a single table (Prof_ID, Course, Hobby) creates which issue?
multivalued dependencies
Medium
A.A violation of the domain integrity rule
B.Partial dependency
C.Transitive dependency
D.Multivalued dependency resulting in a Cartesian product of courses and hobbies
Correct Answer: Multivalued dependency resulting in a Cartesian product of courses and hobbies
Explanation:
Because courses and hobbies are independent, storing them together forces the table to list every combination of a professor's courses and hobbies to maintain consistency, causing massive redundancy.
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39A relation is said to be in Fourth Normal Form (4NF) if it is in BCNF and contains no:
4NF deals specifically with multivalued dependencies. A table is in 4NF if it is in BCNF and possesses no non-trivial multivalued dependencies.
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40To resolve a 4NF violation in the table where an employee has multiple independent skills and speaks multiple independent languages, how should be decomposed?
fourth normal form
Medium
A. and
B. with a new surrogate primary key
C. and
D. and
Correct Answer: and
Explanation:
To eliminate the multivalued dependencies, the relation must be decomposed into two separate tables that independently associate the determinant (Employee) with each multivalued attribute.
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41Consider a relation schema and the set of functional dependencies . Which of the following sets correctly identifies ALL the candidate keys of ?
functional dependency
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
To find candidate keys, compute closures: (so is a key). (so is a key). and , but (so is a key). (so is a key). All four are minimal superkeys.
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42Which of the following represents the canonical cover (minimal cover) for the set of functional dependencies ?
functional dependency
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The correct option follows directly from the given concept and definitions.
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43Given the functional dependencies and for a relation . According to Armstrong's Axioms, which of the following is a valid logical implication?
functional dependency
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Using the augmentation rule on , we get . We are given . Applying the transitivity rule to and , we derive . This specific derivation is known as the pseudo-transitivity rule.
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44In a relational database, Table A and Table B have a cyclic referential integrity constraint (Table A references Table B, and Table B references Table A). Both tables are initially empty. Which of the following is the standard SQL mechanism to successfully insert the first row without violating data integrity rules?
data integrity rules
Hard
A.Insert the rows using a FULL OUTER JOIN statement.
B.Use the ON UPDATE CASCADE clause on both foreign keys.
C.Use DEFERRED constraint checking during a transaction.
D.It is impossible; the schema must be redesigned to remove the cycle.
Correct Answer: Use DEFERRED constraint checking during a transaction.
Explanation:
Cyclic dependencies prevent standard row-by-row insertion because the first row inserted will fail the foreign key check. Deferring constraints (INITIALLY DEFERRED) allows the database to wait until the end of the transaction to check referential integrity, at which point both rows exist.
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45Consider a self-referencing table Employee(EmpID, Name, ManagerID) where ManagerID is a foreign key referencing EmpID. The foreign key is configured with ON DELETE CASCADE. If the database contains a strict hierarchy of 10 employees under one CEO, and the CEO's record (where ManagerID is NULL) is deleted, what is the outcome?
data integrity rules
Hard
A.The database will throw a cycle violation error and abort the transaction.
B.All 11 records (CEO + 10 employees) will be deleted.
C.The deletion will fail due to entity integrity rules.
D.Only the CEO's record is deleted; the employees' ManagerID becomes NULL.
Correct Answer: All 11 records (CEO + 10 employees) will be deleted.
Explanation:
Because the foreign key is defined with ON DELETE CASCADE, deleting the CEO record will cascade to the records referencing the CEO (direct reports). This process continues recursively down the hierarchy, resulting in the deletion of all subordinate records.
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46A relation is decomposed into and . Which of the following conditions strictly guarantees that this decomposition is a lossless-join decomposition?
need of normalization
Hard
A.The union of attributes in and is equal to .
B.The functional dependency or is in .
C.The intersection of attributes in and is not empty.
D. and are in .
Correct Answer: The functional dependency or is in .
Explanation:
A decomposition of into and is lossless if or . Since , the condition requires that (implying ) or (implying ) holds.
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47Which of the following scenarios best illustrates the presence of 'spurious tuples' caused by an inadequate database design?
need of normalization
Hard
A.Failing to update all instances of a redundant value, leading to inconsistent data.
B.A query returning duplicate rows because DISTINCT was not used.
C.Joining two decomposed relations on an attribute that is not a candidate key in either relation.
D.Inserting a partial record into a relation containing multiple independent themes.
Correct Answer: Joining two decomposed relations on an attribute that is not a candidate key in either relation.
Explanation:
Spurious tuples are artificially generated invalid rows that appear when two tables are joined (using natural join) on attributes that do not constitute a primary/candidate key in at least one of the tables, indicating a lossy decomposition.
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48A relation has a primary key . Attribute contains a set of values (a repeating group). To convert to First Normal Form (1NF), a new tuple is created for every value in . What is the primary key of the resulting 1NF relation?
first normal form
Hard
A.The composite key
B.The original key
C.A newly generated surrogate key is strictly required.
D.The composite key
Correct Answer: The composite key
Explanation:
Because flattening the repeating group results in multiple tuples with the same value for and , alone is no longer unique. Assuming the values in are unique for a given , the new primary key must be the combination to ensure entity integrity in 1NF.
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49Consider a relation schema with functional dependencies , , and . The only candidate key is . Which specific functional dependency causes a violation of Second Normal Form (2NF)?
second normal form
Hard
A.
B.None, it is in 2NF.
C.
D.
Correct Answer:
Explanation:
2NF requires that no non-prime attribute is partially dependent on any candidate key. The candidate key is . Attribute depends on , which is only a part of the candidate key . Thus, is a partial dependency violating 2NF.
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50If a relation is in First Normal Form (1NF) and its primary key consists of a single attribute, which of the following statements is unconditionally true?
second normal form
Hard
A.The relation is automatically in Second Normal Form (2NF).
B.The relation contains no transitive dependencies.
C.The relation cannot have any multivalued dependencies.
D.The relation is automatically in Third Normal Form (3NF).
Correct Answer: The relation is automatically in Second Normal Form (2NF).
Explanation:
A violation of 2NF occurs when a non-prime attribute depends on part of a candidate key. If the candidate key consists of a single attribute, it cannot be partitioned. Therefore, partial dependencies are impossible, and the relation is automatically in 2NF.
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51Consider the relation and the set of functional dependencies . What is the highest normal form satisfied by relation ?
third normal form
Hard
A.1NF
B.2NF
C.BCNF
D.3NF
Correct Answer: 3NF
Explanation:
To find candidate keys: , , . The prime attributes are . Because all attributes are prime, there are no non-prime attributes to be transitively dependent on a key. Thus, it satisfies 3NF. However, it violates BCNF because holds, but is not a superkey.
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52In the context of the 3NF synthesis algorithm (Bernstein's algorithm), which of the following guarantees is provided that is NOT always possible when decomposing into Boyce-Codd Normal Form (BCNF)?
third normal form
Hard
A.Dependency Preservation
B.Removal of multi-valued dependencies
C.Elimination of all update anomalies
D.Lossless Join
Correct Answer: Dependency Preservation
Explanation:
The 3NF synthesis algorithm guarantees both a lossless join and dependency preservation. In contrast, decomposing a relation into BCNF guarantees a lossless join, but it is not always possible to preserve all functional dependencies.
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53A relation is strictly in 3NF but not in BCNF. According to the definitions of normal forms, which of the following conditions MUST exist in ?
third normal form
Hard
A.A non-prime attribute is partially dependent on a composite candidate key.
B.A non-prime attribute is functionally dependent on a non-superkey.
C.A non-trivial multivalued dependency exists.
D.A prime attribute is functionally dependent on a non-superkey.
Correct Answer: A prime attribute is functionally dependent on a non-superkey.
Explanation:
In 3NF, for every functional dependency , either is a superkey, or is a prime attribute. If it violates BCNF, there must be an FD where is NOT a superkey. Therefore, to satisfy 3NF while violating BCNF, the right side MUST be a prime attribute.
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54Consider a relation with functional dependencies and . If we attempt to decompose to achieve BCNF, what is the primary consequence of this decomposition?
boyce codd normal form
Hard
A.The resulting tables will violate 4NF.
B.The functional dependency will be lost.
C.The decomposition will result in a lossy join.
D.The functional dependency will be lost.
Correct Answer: The functional dependency will be lost.
Explanation:
Candidate keys for are and . violates BCNF because is not a superkey. Decomposing based on yields and . The FD spans across and and cannot be enforced without joining the tables, so it is not preserved.
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55Let be a relation with exactly one candidate key, . Which of the following functional dependencies would NOT cause a violation of BCNF?
boyce codd normal form
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
BCNF requires that for every non-trivial functional dependency , must be a superkey. Since is the candidate key, has a superkey on the left-hand side, so it satisfies BCNF. All other options have non-superkeys (, , or ) on the left-hand side, which would violate BCNF.
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56Which of the following statements about relations with exactly two attributes is strictly mathematically proven?
boyce codd normal form
Hard
A.A relation with exactly two attributes can violate BCNF if there is a transitive dependency.
B.Any relation with exactly two attributes is always in BCNF.
C.A relation with two attributes is in BCNF only if both attributes form the primary key.
D.A relation with exactly two attributes may be in 3NF but fail BCNF.
Correct Answer: Any relation with exactly two attributes is always in BCNF.
Explanation:
Let the relation be . The possible non-trivial FDs are or . If holds, is a candidate key. If holds, is a candidate key. In all cases where a non-trivial FD holds, its left side is a superkey. Therefore, no BCNF violation can ever exist.
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57Given a relation schema . If the multivalued dependency holds, what other dependency is logically guaranteed to hold according to the complementation rule of multivalued dependencies?
multivalued dependencies
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The complementation rule for multivalued dependencies states that if holds on schema , then also holds. Since , . Therefore, must hold.
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58A multivalued dependency in a relation is defined as 'trivial' if and only if which of the following conditions is met?
multivalued dependencies
Hard
A. is a candidate key of
B. or
C. is a single attribute
D. and
Correct Answer: or
Explanation:
A multivalued dependency is trivial if is a subset of () or if and together make up the entire relation schema (). In these cases, the MVD holds naturally without constraining the data.
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59Consider a relation CourseInfo(Course, Teacher, Book). A course can have multiple teachers and multiple recommended books. Teachers and books are completely independent of each other for a given course. The relation currently has no functional dependencies. Which normal form does CourseInfo violate?
fourth normal form
Hard
A.Third Normal Form (3NF)
B.Boyce-Codd Normal Form (BCNF)
C.Second Normal Form (2NF)
D.Fourth Normal Form (4NF)
Correct Answer: Fourth Normal Form (4NF)
Explanation:
The table lacks any non-trivial functional dependencies, meaning the only candidate key is the combination (Course, Teacher, Book). Thus, it is in BCNF. However, because Teachers and Books are independent multi-valued attributes, there are non-trivial MVDs: and . Because 'Course' is not a superkey, this violates 4NF.
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60Let be a relation schema that is certified to be in Fourth Normal Form (4NF). Which of the following MUST necessarily be true regarding ?
fourth normal form
Hard
A. cannot be decomposed any further without losing data.
B.For every non-trivial functional dependency , is a superkey.
C. has exactly one candidate key.
D.There are no functional dependencies of any kind in .
Correct Answer: For every non-trivial functional dependency , is a superkey.
Explanation:
4NF is a stricter normal form than BCNF. A relation in 4NF is guaranteed to be in BCNF. The definition of BCNF is that for every non-trivial functional dependency , must be a superkey. Therefore, this property must hold true for any relation in 4NF.