CS 6400 EXAM 3 QUESTIONS AND
ANSWERS 2026/2027 GRADED A+
Course
Db Sys Concepts& Design
1. Which statement correctly describes a functional dependency X → Y?
A. X and Y must both be primary keys
B. The value of X uniquely determines the value of Y
C. Y must always be a foreign key
D. X and Y must contain the same attributes
Answer: B. The value of X uniquely determines the value of Y
Rationale: X → Y means that whenever two tuples have the same values for X, they must also
have the same values for Y.
2. Which of Armstrong's inference rules is represented by X → Y and Y → Z, therefore X
→ Z?
A. Reflexivity
B. Augmentation
C. Transitivity
D. Decomposition
Answer: C. Transitivity
Rationale: The transitivity rule states that if X determines Y and Y determines Z, then X
determines Z.
3. What does Armstrong's reflexivity rule state?
A. If X → Y, then XZ → YZ
B. If Y ⊆ X, then X → Y
C. If X → Y and Y → Z, then X → Z
D. If X → YZ, then X → Y
Answer: B. If Y ⊆ X, then X → Y
Rationale: Reflexivity establishes trivial functional dependencies where the attributes on the
right side are already contained in the determinant.
4. What is the augmentation rule?
A. If X → Y, then XZ → YZ
B. If X → Y and Y → Z, then X → Z
,C. If Y ⊆ X, then X → Y
D. If X → YZ, then X → Z
Answer: A. If X → Y, then XZ → YZ
Rationale: Augmentation allows the same additional attributes to be added to both sides of a
functional dependency.
5. What is a candidate key?
A. Any attribute that contains duplicate values
B. A minimal set of attributes that uniquely identifies each tuple
C. Every foreign key in a relation
D. An attribute that must contain NULL
Answer: B. A minimal set of attributes that uniquely identifies each tuple
Rationale: A candidate key uniquely identifies tuples and is minimal, meaning no attribute can
be removed while retaining uniqueness.
6. What distinguishes a superkey from a candidate key?
A. A superkey cannot identify tuples
B. A candidate key can contain duplicate values
C. A superkey may contain unnecessary attributes
D. A candidate key must always be a foreign key
Answer: C. A superkey may contain unnecessary attributes
Rationale: Every candidate key is a superkey, but a superkey does not have to be minimal.
7. Consider R(A, B, C) with dependencies A → B and B → C. What attributes can be
determined by A+?
A. A only
B. A and B only
C. A, B, and C
D. B and C only
Answer: C. A, B, and C
Rationale: Starting with A, A → B gives B, and B → C then gives C. Therefore A+ = {A, B, C}.
8. What is the primary purpose of computing an attribute closure?
A. To determine whether a set of attributes can determine other attributes
B. To calculate disk space
, C. To identify duplicate tuples
D. To calculate transaction duration
Answer: A. To determine whether a set of attributes can determine other attributes
Rationale: Attribute closure is used to determine all attributes functionally determined by a
given attribute set and is useful for finding candidate keys.
9. What is normalization primarily intended to reduce?
A. Network bandwidth
B. Data redundancy and modification anomalies
C. CPU speed
D. Number of database users
Answer: B. Data redundancy and modification anomalies
Rationale: Normalization organizes relations to reduce unnecessary duplication and problems
such as insertion, deletion, and update anomalies.
10. Which anomaly occurs when updating one fact requires changing the same fact in
multiple rows?
A. Insertion anomaly
B. Deletion anomaly
C. Update anomaly
D. Join anomaly
Answer: C. Update anomaly
Rationale: Redundant data can become inconsistent when only some copies are updated.
11. Which anomaly occurs when deleting a tuple unintentionally removes information about
another fact?
A. Update anomaly
B. Deletion anomaly
C. Insertion anomaly
D. Projection anomaly
Answer: B. Deletion anomaly
Rationale: A poorly designed relation may combine unrelated facts so that deleting one fact also
eliminates information that should have been retained.
12. Which anomaly occurs when a fact cannot be inserted without also inserting unrelated
information?
ANSWERS 2026/2027 GRADED A+
Course
Db Sys Concepts& Design
1. Which statement correctly describes a functional dependency X → Y?
A. X and Y must both be primary keys
B. The value of X uniquely determines the value of Y
C. Y must always be a foreign key
D. X and Y must contain the same attributes
Answer: B. The value of X uniquely determines the value of Y
Rationale: X → Y means that whenever two tuples have the same values for X, they must also
have the same values for Y.
2. Which of Armstrong's inference rules is represented by X → Y and Y → Z, therefore X
→ Z?
A. Reflexivity
B. Augmentation
C. Transitivity
D. Decomposition
Answer: C. Transitivity
Rationale: The transitivity rule states that if X determines Y and Y determines Z, then X
determines Z.
3. What does Armstrong's reflexivity rule state?
A. If X → Y, then XZ → YZ
B. If Y ⊆ X, then X → Y
C. If X → Y and Y → Z, then X → Z
D. If X → YZ, then X → Y
Answer: B. If Y ⊆ X, then X → Y
Rationale: Reflexivity establishes trivial functional dependencies where the attributes on the
right side are already contained in the determinant.
4. What is the augmentation rule?
A. If X → Y, then XZ → YZ
B. If X → Y and Y → Z, then X → Z
,C. If Y ⊆ X, then X → Y
D. If X → YZ, then X → Z
Answer: A. If X → Y, then XZ → YZ
Rationale: Augmentation allows the same additional attributes to be added to both sides of a
functional dependency.
5. What is a candidate key?
A. Any attribute that contains duplicate values
B. A minimal set of attributes that uniquely identifies each tuple
C. Every foreign key in a relation
D. An attribute that must contain NULL
Answer: B. A minimal set of attributes that uniquely identifies each tuple
Rationale: A candidate key uniquely identifies tuples and is minimal, meaning no attribute can
be removed while retaining uniqueness.
6. What distinguishes a superkey from a candidate key?
A. A superkey cannot identify tuples
B. A candidate key can contain duplicate values
C. A superkey may contain unnecessary attributes
D. A candidate key must always be a foreign key
Answer: C. A superkey may contain unnecessary attributes
Rationale: Every candidate key is a superkey, but a superkey does not have to be minimal.
7. Consider R(A, B, C) with dependencies A → B and B → C. What attributes can be
determined by A+?
A. A only
B. A and B only
C. A, B, and C
D. B and C only
Answer: C. A, B, and C
Rationale: Starting with A, A → B gives B, and B → C then gives C. Therefore A+ = {A, B, C}.
8. What is the primary purpose of computing an attribute closure?
A. To determine whether a set of attributes can determine other attributes
B. To calculate disk space
, C. To identify duplicate tuples
D. To calculate transaction duration
Answer: A. To determine whether a set of attributes can determine other attributes
Rationale: Attribute closure is used to determine all attributes functionally determined by a
given attribute set and is useful for finding candidate keys.
9. What is normalization primarily intended to reduce?
A. Network bandwidth
B. Data redundancy and modification anomalies
C. CPU speed
D. Number of database users
Answer: B. Data redundancy and modification anomalies
Rationale: Normalization organizes relations to reduce unnecessary duplication and problems
such as insertion, deletion, and update anomalies.
10. Which anomaly occurs when updating one fact requires changing the same fact in
multiple rows?
A. Insertion anomaly
B. Deletion anomaly
C. Update anomaly
D. Join anomaly
Answer: C. Update anomaly
Rationale: Redundant data can become inconsistent when only some copies are updated.
11. Which anomaly occurs when deleting a tuple unintentionally removes information about
another fact?
A. Update anomaly
B. Deletion anomaly
C. Insertion anomaly
D. Projection anomaly
Answer: B. Deletion anomaly
Rationale: A poorly designed relation may combine unrelated facts so that deleting one fact also
eliminates information that should have been retained.
12. Which anomaly occurs when a fact cannot be inserted without also inserting unrelated
information?
