Functional Dependencies & Normalization Practice | Digiimento

Question 1: Functional Dependencies

Suppose the following functional dependencies hold on a relation V with attributes A, B, C, D, and E:

• A → BC
• CD → E

Which of the following functional dependencies can be inferred from the above functional dependencies?

1. AD → E
2. C → E
3. A → C
4. AD → B

Question 2: Relational Data Model

In a relational data model, which one of the following statements is TRUE?

1. A relation with only two attributes is always in 3NF.
2. If all attributes of a relation are prime attributes, then the relation is in 3NF.
3. Every relation has at least one non-prime attribute.
4. 3NF decompositions preserve functional dependencies.

Question 4: Functional Dependency Context

The symbol → indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

1. (M, N) → (O, P) implies M → (O, P).
2. (M, N) → (O, P) implies (M, N) → O.
3. ((M, N) → O and P → N) implies (M, P) → O.
4. (M → N and N → O) implies M → O.

Question 3: First Normal Form (1NF)

Which of the following statements about a relation S in first normal form (1NF) is/are TRUE?

1. S can have a multi-attribute key.
2. S cannot have a foreign key.
3. S cannot have a composite attribute.
4. S cannot have more than one candidate key.

Question 5: Relational Schema and Functional Dependencies

Given the relational schema T = (A, B, C, D, E, F) and the set of functional dependencies:

{A → B, A → C, CD → E, CD → F, B → D}

Which of the following functional dependencies can be derived from the above set?

1. BC → EF
2. AC → EF
3. BC → A
4. BC → F

Question 6: Relation Instances

Given the following relation instances:

A	B	C
1	3	2
1	4	3
1	3	4
2	5	4
3	2	1

Which of the following conditions is/are TRUE?

1. AB → C and C → B
2. BC → A and A → C
3. B → A and B →> A
4. AC → B and B → A

Question 7: Normalization in Relational Schema

A relation EmpData is defined with attributes emp_id (unique), name, street, city, state, and zipcode. For any given zipcode, there is exactly one city and state. Also, for any given street and city, there is exactly one zipcode.

In terms of normalization, the relation is in:

1. 1NF only
2. 2NF and hence also in 1NF
3. 3NF and hence also in 2NF and 1NF
4. BCNF and hence also in 3NF, 2NF, and 1NF

Question 8: Normal Forms and Functional Dependencies

A table has fields T1, T2, T3, T4, T5 with the following functional dependencies:

• T1 → T3
• T2 → T4
• (T1, T2) → T5

In terms of normalization, this table is in:

1. 1NF
2. 2NF
3. 3NF
4. None of the above

Question 9: Functional Dependencies in Schema

In a schema with attributes P, Q, R, S, T and the following set of functional dependencies:

• P → Q
• P → R
• RS → T
• Q → S
• T → P

Which of the following functional dependencies is NOT implied by the above set?

1. RS → PR
2. QS → RS
3. PR → QS
4. PS → QR

Question 10: Candidate Key Determination

Consider a relation T with five attributes P, Q, R, S, T. The following functional dependencies hold:

• PR → Q
• QS → T
• ST → P

Which of the following is a candidate key for T?

1. PQS
2. PRT
3. QST
4. PQRST

Question 11: Functional Dependencies and Normalization

A table has fields A1, A2, A3, A4, A5 with the following functional dependencies:

• A1 → A3
• A2 → A4
• (A1, A2) → A5

In terms of Normalization, this table is in:

1. 1NF
2. 2NF
3. 3NF
4. None of these

Question 12: Functional Dependencies in Schema

In a schema with attributes P, Q, R, S, T and the following set of functional dependencies:

• P → Q
• P → R
• RS → T
• Q → S
• T → P

Which of the following functional dependencies is NOT implied by the above set?

1. RS → PQ
2. PR → RS
3. QS → RP
4. PT → QS

Question 13: Candidate Key for Relation

Consider a relation T with five attributes A, B, C, D, E. The following functional dependencies hold:

• AB → C
• CD → E
• DE → A

Which of the following is a candidate key for T?

1. ACE
2. ABD
3. BCD
4. ABCDE

Question 14: Lossless Join and Dependency Preservation

Let R(A, B, C, D) be a relational schema with the following functional dependencies:

• A → B
• B → C
• C → D
• D → B

The decomposition of R into (A, B), (B, C), (B, D)

Which of the following is correct?

1. gives a lossless join, and is dependency preserving
2. gives a lossless join, but is not dependency preserving
3. does not give a lossless join, but is dependency preserving
4. does not give a lossless join and is not dependency preserving

Question 15: Normal Forms of Schema

Let R(A, B, C, D, E, F, G) be a relational schema in which the following functional dependencies are known to hold:

• AB → CD
• DE → F
• C → E
• F → C
• B → G

The relational schema R is:

1. in BCNF
2. in 3NF, but not in BCNF
3. in 2NF, but not in 3NF
4. not in 2NF