Multivalued Dependency (MVD) and 4NF MCQs: 12 Solved Questions

MVD questions resemble ordinary normalization questions, but functional, multivalued and join dependencies differ. A BCNF relation may still repeat every hobby-language combination for one student. Solve these 12 MCQs before reading the explanations. The earlier DBMS Normalization MCQs owns mixed practice from 1NF through BCNF; this set concentrates on MVD rules and 4NF decompositions beyond BCNF.

1. MVD and 4NF in one worked relation

Student -> Hobby means each student determines one hobby. Student ↠ Hobby means the hobby set varies independently of the remaining attributes. Every FD implies its corresponding MVD, but not conversely. This is where 4NF goes beyond the FD-based forms in Normalization in DBMS: 1NF to BCNF.

A relation is in 4NF only when, for every non-trivial MVD X ↠ Y in R, X must be a superkey. Consider R(Student, Hobby, Language) and Student = 101:

Here the hobby and language sets are independent. Therefore Student ↠ Hobby; complementation gives Student ↠ Language. Student is not a superkey because it identifies four rows. The first MVD is non-trivial: Hobby is not contained in Student, and Student ∪ Hobby is not all of R. Thus R violates 4NF even if it satisfies BCNF.

Decompose into R1(Student, Hobby) = {(101, Chess), (101, Guitar)} and R2(Student, Language) = {(101, Hindi), (101, English)}. Their natural join pairs two hobbies with two languages: 2 x 2 = 4 original tuples. The lossless decomposition stores each independent fact once. The earlier Lossless Join Decomposition MCQs: 12 Solved Questions with Explanations owns the general binary and multi-relation reconstruction tests; this example isolates the MVD-specific split used by 4NF.

2. MCQs 1-3: what 4NF removes and where BCNF stops

Question 1

TPSC 2026.

In database normalization, what problem does 4NF (Fourth Normal Form) address ?

• A. Partial dependencies

• B. Transitive dependencies

• C. Multi-valued dependencies

• D. Join dependencies

Answer: C. 2NF targets partial dependencies, 3NF transitive dependencies, 4NF violating non-trivial MVDs and 5NF non-trivial join dependencies. Trivial and superkey-determined MVDs are allowed in 4NF.

Question 2

Kendriya Vidyalaya Sangathan 2013.

If a table is in BCNF and has no multi-valued dependencies, then it is said to be in

• A. Third Normal Form

• B. Second Normal Form

• C. Fourth Normal Form

• D. Fifth Normal Form

Answer: C. “No multi-valued dependencies” means no violating non-trivial MVD. BCNF covers FDs; the added condition gives 4NF, while 5NF tests join dependencies.

Question 3

UGC NET 2019.

In relational databases, if relation R is in BCNF, then which of the following is true about relation R?

• A. R is in 4NF

• B. R is not in 1NF

• C. R is in 2NF and not in 3NF

• D. R is in 2NF and 3NF

Answer: D. BCNF implies 3NF and 2NF, but not necessarily 4NF, which also tests non-trivial MVDs.

3. MCQs 4-6: the formal 4NF rule and the normalization ladder

Question 4

Which of the following statements about fourth normal form (4NF) is true?

• A. A relation in 4NF must be in BCNF and should not have any non-trivial MVDs.

• B. A relation in 4NF must be in 3NF and should have only trivial MVDs.

• C. A relation in 4NF must be in 2NF and should not have any trivial MVDs.

• D. A relation in 4NF must be in BCNF and can have non-trivial MVDs.

Answer: D. As written, D is correct: 4NF permits a non-trivial MVD when its determinant is a superkey. The linked question labels A, but A is too broad because it forbids every non-trivial MVD instead of only the violating ones.

Question 5

UGC NET 2022.

Match List I with List II :

$\begin{array}{ll} \text{List I} & \text{List II} \\ \\ \text {(A) BCNF } & \text { (I) It removes multivalued dependency } \\ \text {(B) 3} \mathrm{NF} & \text { (II) It is not always dependency preserving } \\ \text {(C) 2} \mathrm{NF} & \text{ (III) It removes transitive dependency} \\ \text {(D) 4} \mathrm{NF} & \text { (IV) It removes partial functional dependency }\end{array}$

Choose the correct answer from the options given below:

• A. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)

• B. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)

• C. (A)-(II), (B)-(III), (C)-(IV), (D)-(I)

• D. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

Answer: C. Match BCNF with not always dependency preserving, 3NF with transitive dependency, 2NF with partial functional dependency, and 4NF with violating MVDs.

Question 6

UGC NET 2023.

Which of the follwing are true?

A. A database design is in BCNF if each member of the set of relation schemas that constitutes the design is in BCNF.

B. A BCNF schema can have transitive dependency.

C. It is always possible to obtain a 3NF design without sacrificing a lossless join.

D. There are multivalued dependencies in 4NF.

• A. A, B and C only

• B. B, C and D only

• C. A, B and D only

• D. A, C and D only

Answer: D. A holds schema by schema; B is false here; C follows from 3NF synthesis. D holds because trivial and superkey-determined MVDs remain.

4. MCQs 7-9: where MVDs come from and what they imply

Question 7

Tech Mahindra 2024.

If a multivalued dependency holds and is not implied by the corresponding functional dependency, it usually arises from one of the following sources.

• A. A many-to-many relationship set

• B. A multivalued attribute of an entity set

• C. A one-to-many relationship set

• D. Both A many-to-many relationship set and A multivalued attribute of an entity set

Answer: D. Many-to-many relationships and multivalued attributes can form independent value sets. One-to-many more naturally gives a directional FD.

Question 8

Tech Mahindra 2023.

Which of the following is a tuple-generating dependency?

• A. Functional dependency

• B. Equality-generating dependency

• C. Multivalued dependency

• D. Non-functional dependency

Answer: C. (101, Chess, Hindi) and (101, Guitar, English) require (101, Chess, English) and (101, Guitar, Hindi). This required tuple existence makes an MVD tuple-generating; an FD enforces equality.

Question 9

GATE 2007.

Consider the following implications relating to functional and multivalued dependencies given below, which may or may not be correct.

i. If A ↠ B and A ↠ C then A → BC

ii. If A → B and A → C then A ↠ BC

iii. If A ↠ BC and A → B then A → C

iv. If A → BC and A → B then A ↠ C

Exactly how many of the above implications are valid?

• A. 0

• B. 1

• C. 2

• D. 3

Answer: C. Exactly ii and iv hold. Union gives A -> BC, then its MVD; decomposition gives A -> C, then its MVD. Statement i promotes MVDs to an FD; in iii, A ↠ BC can be trivial while several C values remain.

5. MCQs 10-12: decomposition, hierarchy and wording traps

Question 10

UGC NET 2025.

Which of the following/s is/are FALSE statement?

A. An all key relation is always in BCNF since it has no FDs.

B. A relation that is not in 4NF due to nontrivial MVD must be decomposed to convert it into a set of relations in 4NF.

C. The decomposition removes the redundancy by the MVD.

D. 3NF is stronger than BCNF.

Choose the correct answer from the options given below:

• A. A only

• B. A, B only

• C. D only

• D. C only

Answer: C. D alone is false because BCNF is stronger. Under the intended all-key, no-non-trivial-FD reading, A is true. B and C remove MVD redundancy by decomposition.

Question 11

UGC NET 2005.

Match the following:

• A. i- (a) ii-(c) iii-(b) iv-(d)

• B. i-(d) ii-(c) iii-(a) iv-(b)

• C. i-(d) ii-(c) iii-(b) iv-(a)

• D. i-(d) ii-(c) iii-(b) iv-(a)

Answer: B. Match 5NF -> (d), 2NF -> (c), 3NF -> (a), and 4NF -> (b). Options C and D here are printed identically. “No join dependency” means no violating non-trivial one.

Question 12

UGC NET 2014.

Which of the following is false?

• A. Every binary relation is never be in BCNF.

• B. Every BCNF relation is in 3NF.

• C. 1 NF, 2 NF, 3 NF and BCNF are based on functional dependencies.

• D. Multivalued Dependency (MVD) is a special case of Join Dependency (JD).

Answer: A. In a binary relation, a non-trivial FD's determinant becomes a key; without one, no BCNF violation exists. B, C and D are true.

6. Four recurring traps in 4NF questions

For the worked values, R1 ⋈ R2 pairs two hobbies with two languages and returns four tuples without missing or spurious combinations.

7. 4NF recall and practice

• Every FD implies an MVD.

• The converse is false.

• Independent multivalued facts create a Cartesian-style cross-product.

• 4NF checks the determinants of non-trivial MVDs.

• A non-superkey determinant violates 4NF.

• Decompose, then verify a lossless join.

Allow 18 minutes for these 12 questions. Label each miss normal-form hierarchy, FD versus MVD, inference rule, source of MVD or decomposition. For decomposition practice, redraw the four-tuple Student relation and explain each recombined tuple.

For a sequenced GATE route, continue with GATE Guidance by Sanchit Sir. Placement-focused readers rebuilding DBMS alongside OS and Computer Networks can use CS Fundamentals for Placements as the broader category route.