The Relational Model and Normalization Questions and Answers

Q: In a relational database, what is a "tuple" ?

A tuple is A row in a table.In the relational model, a relation is a table, each tuple is one row (a record), and each attribute is a column.A column is an attribute, a table is a relation, and a database is a collection of relations.The number of tuples in a relation is called its cardinality, and the number of attributes its degree.

Q: Which of the following is true about "referential integrity" ?

Referential integrity ensures that foreign keys are valid and correspond to primary keys.It requires every non-null foreign key value in one table to match an existing primary key value in the table it refers to, so there are no orphan records, such as an order for a customer who does not exist.Preventing nulls is the NOT NULL constraint, preventing duplicates is the job of primary key or UNIQUE constraints, and referential integrity is a central part of the relational model.

Q: Which normal form eliminates transitive dependencies ?

Transitive dependencies are removed by 3NF (third normal form).A relation is in 3NF when it is in 2NF and no non-key attribute depends on the key through another non-key attribute. For example, in Student(id, dept, dept_head), dept_head depends on id only through dept, so it is moved into a separate Department table.1NF requires atomic values. 2NF removes partial dependencies on part of a composite key. BCNF is a stricter form that also handles dependencies whose determinant is not a superkey, but the normal form defined by removing transitive dependencies is 3NF.

Q: What is the degree of a relation in a relational database ?

The degree of a relation is the number of attributes.In the relational model, degree (also called arity) counts the columns of a relation. A table Student(roll, name, age) has degree 3 whatever the number of rows.The number of tuples, or rows, is the relation's cardinality, the usual trap here. The number of keys and the number of constraints are not standard measures of a relation's size.

Q: Which of the following is TRUE ?

The true statement is Every relation in BCNF is also in 3NF.BCNF requires that every nontrivial functional dependency X → A has X as a superkey. 3NF allows one extra case, where A is a prime attribute. So BCNF is the stricter form, and any BCNF relation automatically satisfies 3NF.The reverse, every 3NF relation being in BCNF, is false. Option B describes 2NF-style full dependence, not the definition of 3NF. And a relation can certainly be in both, since every BCNF relation is.

Q: Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, N} and the set of functional; dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N}} on R. What is the key for R ?

The key is {E, F, H}.E, F and H never appear on the right-hand side of any dependency, so every key must contain them. Their closure is the whole relation:{E, F} → G, and F → I, J;{E, H} → K, L;K → M and L → N.So {E, F, H} determines all ten attributes and is minimal. {E, F} and {E} miss H, K, L, M and N. {E, F, H, K, L} is a superkey but not minimal, because K and L follow from E and H.

Q: Which normal form is considered adequate for normal relational database design ?

The normal form considered adequate is 3 NF.Third normal form removes partial and transitive dependencies on keys, which eliminates most redundancy and update anomalies, and a lossless, dependency-preserving decomposition into 3NF can always be found. It is therefore the usual target for practical relational design.1NF and 2NF leave too much redundancy. BCNF is stricter, but a BCNF decomposition may lose some functional dependencies, so it is not always the practical goal.

Q: Referential Integrity constraints functions using the __________ concept.

Referential integrity works through the Foreign key.A referential integrity constraint says a value in one table must match a value in the table it refers to, for example every order's customer_id must exist in the customers table. The referring column is a foreign key, which references the primary key of the other table.The primary key ensures each row of its own table is unique, a super key is any set of attributes that identifies rows, and a secondary key is an alternative search key. None of them links tables the way a foreign key does.

Q: In Relational Algebra, which operator is NOT primitive but derived ?

The derived operator is Join.The primitive (fundamental) operations of relational algebra are selection, projection, union, set difference, Cartesian product and rename. A join is not one of them, because it can be written in terms of them: a theta join is a selection applied to a Cartesian product, and a natural join adds a projection to remove the duplicate columns.Selection, projection and Cartesian product are all primitive, so none of them is the answer.

Q: For a relation R(A, B, C) with three attributes A, B and C, what is the maximum number of possible composite keys ?

The maximum number of composite keys is 4.A composite key is a key made of two or more attributes. From three attributes the possible combinations of two or more are:\[ \begin{aligned} &\{A,B\},\ \{A,C\},\ \{B,C\} \\ &\{A,B,C\} \end{aligned} \]That is \(\binom{3}{2} + \binom{3}{3} = 3 + 1 = 4\). 3 counts only the two-attribute pairs, 7 counts every non-empty subset including the three single attributes, which are not composite, and 9 matches no count.

21.

In a relational database, what is a "tuple" ?

A.A row in a table
B.A column in a table
C.A table
D.A database

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: A

A tuple is A row in a table.

In the relational model, a relation is a table, each tuple is one row (a record), and each attribute is a column.

A column is an attribute, a table is a relation, and a database is a collection of relations.

The number of tuples in a relation is called its cardinality, and the number of attributes its degree.

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22.

Which of the following is true about "referential integrity" ?

A.It ensures that foreign keys are valid and correspond to primary keys.
B.It prevents the insertion of null values in a table.
C.It allows duplicate entries in a table.
D.It is unrelated to the relational database model.

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: A

Referential integrity ensures that foreign keys are valid and correspond to primary keys.

It requires every non-null foreign key value in one table to match an existing primary key value in the table it refers to, so there are no orphan records, such as an order for a customer who does not exist.

Preventing nulls is the NOT NULL constraint, preventing duplicates is the job of primary key or UNIQUE constraints, and referential integrity is a central part of the relational model.

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23.

Which normal form eliminates transitive dependencies ?

A.1NF
B.2NF
C.3NF
D.BCNF

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

Transitive dependencies are removed by 3NF (third normal form).

A relation is in 3NF when it is in 2NF and no non-key attribute depends on the key through another non-key attribute. For example, in Student(id, dept, dept_head), dept_head depends on id only through dept, so it is moved into a separate Department table.

1NF requires atomic values. 2NF removes partial dependencies on part of a composite key. BCNF is a stricter form that also handles dependencies whose determinant is not a superkey, but the normal form defined by removing transitive dependencies is 3NF.

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24.

What is the degree of a relation in a relational database ?

A.Number of tuples
B.Number of attributes
C.Number of keys
D.Number of constraints

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: B

The degree of a relation is the number of attributes.

In the relational model, degree (also called arity) counts the columns of a relation. A table Student(roll, name, age) has degree 3 whatever the number of rows.

The number of tuples, or rows, is the relation's cardinality, the usual trap here. The number of keys and the number of constraints are not standard measures of a relation's size.

Discuss in Forum

25.

Which of the following is TRUE ?

A.Every relation in 3NF is also in BCNF.
B.A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R.
C.Every relation in BCNF is also in 3NF.
D.No relation can be in both BCNF and 3NF.

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: C

The true statement is Every relation in BCNF is also in 3NF.

BCNF requires that every nontrivial functional dependency X → A has X as a superkey. 3NF allows one extra case, where A is a prime attribute. So BCNF is the stricter form, and any BCNF relation automatically satisfies 3NF.

The reverse, every 3NF relation being in BCNF, is false. Option B describes 2NF-style full dependence, not the definition of 3NF. And a relation can certainly be in both, since every BCNF relation is.

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26.

Consider the relation scheme R = {E, F, G, H, I, J, K, L, M, N} and the set of functional; dependencies {{E, F} -> {G}, {F} -> {I, J}, {E, H} -> {K, L}, K -> {M}, L -> {N}} on R. What is the key for R ?

A.{E, F}
B.{E, F, H}
C.{E, F, H, K, L}
D.{E}

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: B

The key is {E, F, H}.

E, F and H never appear on the right-hand side of any dependency, so every key must contain them. Their closure is the whole relation:

{E, F} → G, and F → I, J;
{E, H} → K, L;
K → M and L → N.

So {E, F, H} determines all ten attributes and is minimal. {E, F} and {E} miss H, K, L, M and N. {E, F, H, K, L} is a superkey but not minimal, because K and L follow from E and H.

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27.

Which normal form is considered adequate for normal relational database design ?

A.3 NF
B.2 NF
C.1 NF
D.BCNF

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: A

The normal form considered adequate is 3 NF.

Third normal form removes partial and transitive dependencies on keys, which eliminates most redundancy and update anomalies, and a lossless, dependency-preserving decomposition into 3NF can always be found. It is therefore the usual target for practical relational design.

1NF and 2NF leave too much redundancy. BCNF is stricter, but a BCNF decomposition may lose some functional dependencies, so it is not always the practical goal.

Discuss in Forum

28.

Referential Integrity constraints functions using the __________ concept.

A.Primary key
B.Super key
C.Foreign key
D.Secondary key

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: C

Referential integrity works through the Foreign key.

A referential integrity constraint says a value in one table must match a value in the table it refers to, for example every order's customer_id must exist in the customers table. The referring column is a foreign key, which references the primary key of the other table.

The primary key ensures each row of its own table is unique, a super key is any set of attributes that identifies rows, and a secondary key is an alternative search key. None of them links tables the way a foreign key does.

Discuss in Forum

29.

In Relational Algebra, which operator is NOT primitive but derived ?

A.Selection
B.Projection
C.Join
D.Cartesian Product

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

The derived operator is Join.

The primitive (fundamental) operations of relational algebra are selection, projection, union, set difference, Cartesian product and rename. A join is not one of them, because it can be written in terms of them: a theta join is a selection applied to a Cartesian product, and a natural join adds a projection to remove the duplicate columns.

Selection, projection and Cartesian product are all primitive, so none of them is the answer.

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30.

For a relation R(A, B, C) with three attributes A, B and C, what is the maximum number of possible composite keys ?

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: B

The maximum number of composite keys is 4.

A composite key is a key made of two or more attributes. From three attributes the possible combinations of two or more are:

\[ \begin{aligned} &\{A,B\},\ \{A,C\},\ \{B,C\} \\ &\{A,B,C\} \end{aligned} \]

That is \(\binom{3}{2} + \binom{3}{3} = 3 + 1 = 4\). 3 counts only the two-attribute pairs, 7 counts every non-empty subset including the three single attributes, which are not composite, and 9 matches no count.

Discuss in Forum

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