GATE Computer Science Engineering(CSE) 2027 Test: Functional Dependencies

Test: Functional Dependencies & Normalization- 1 - Question 1

Which normal form is considered adequate for relational database design?

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

Detailed Solution: Question 1

3NF is considered to be most adequate for relational database design. It always preserves dependency as compare to BCNF which is more io restrictive form of 3NF. Although it does not eliminates redundancy due to MVD’s but it does satisfies two essential properties.
1. If eliminates redundancy due to FD’s.
2. It preserve FD’s
4NF is not considered to be adequate because it does not preserve FD’s always.

Test: Functional Dependencies & Normalization- 1 - Question 2

If every non-key attribute is functionally dependent on the primary key, then the relation will be in

A.
First normal form
B.
Third normal form
C.
Second normal form
D.
Fourth normal form

Detailed Solution: Question 2

Conditions for various normal forms:

1 NF – A relation R is in first normal form (1NF) if and only if all underlying domains contain atomic values only.
2 NF – A relation R is in second normal form (2NF) if and only if it is in 1NF and every non-key attribute is fully dependent on the primary key.
3 NF – A relation R is in third normal form (3NF) if and only if it is in 2NF and every non-key attribute is non-transitively dependent on the primary key.
BCNF – A relation R is in Boyce-Codd normal form (BCNF) if and only if every determinant is a candidate key.

Example:
Relation R(XYZ) with functional dependencies {X -> Y, Y -> Z, X -> Z}.
Notice here Y -> Z, in question it is not mention that non prime attribute is only dependent on primary key so this FD is perfectly valid.
This relation is in 2NF but not in 3NF because of every non-key attribute is transitively dependent on the primary key. Here {X} will be candidate key.

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Test: Functional Dependencies & Normalization- 1 - Question 3

Given the functional dependencies:
X→W; X→Y; Y→Z and Z→PQ
Which of the following does not hold good?

A.
X→Z
B.
W→Z
C.
X→WY
D.
None of these

Detailed Solution: Question 3

Since there is no FD’s for which W functionally depends on other attributes.

Test: Functional Dependencies & Normalization- 1 - Question 4

For a database relation R(a, b, c, d) where the domains of a, b, c and d include only atomic values, only the following functional dependencies and those that can be inferred from them hold.
a → c
b→d
The relation is in

A.
First normal form but not in second normal form
B.
Second normal form but not in third normal form
C.
Third normal form
D.
None of the above

Detailed Solution: Question 4

Since for Database relation R(a, b, c, d) all values are atomic and

Here neither of a, b, c, d are primary key.
The primary key is 'ab‘ prime attributes = {a, b} here part of key (a in a → c and in b in b → d) is dependent on non key hence there is a partial dependency and the relation is not in 2 NF.
Hence (a) is the correct option

Test: Functional Dependencies & Normalization- 1 - Question 5

Third normal form is inadequate in situations where the relation

A.
Has multiple candidate keys
B.
Has candidate keys that are composite
C.
Has overlapped candidate keys
D.
All of the above

Detailed Solution: Question 5

Third normal form is considered adequate for relational database design, it is inadequate in all situations with the relation having multiple, composes or overlapped candidate keys.

Test: Functional Dependencies & Normalization- 1 - Question 6

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance.
Q. Which is the discriminator of the weak entity?

A.
Account number
B.
Transaction number
C.
{Account number, date}
D.
Date

Detailed Solution: Question 6

We can clearly see that transaction is the weak entity with the discriminator (key for weak entity) as transaction number. This discriminator is used to uniquely identify each transaction of a particular account.

Test: Functional Dependencies & Normalization- 1 - Question 7

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance.
Q. Which is the primary key of the weak entity?

A.
Account number
B.
{Account number, transaction number}
C.
{Account number, date}
D.
{Transaction number, date}

Detailed Solution: Question 7

In order to identify each transaction of any account the key of strong entity with the addition of the discriminator of weak entity can be taken. Here [Account number, transaction number] act as the primary key of weak entity. This is because weak entity has no existence without strong entity.

Test: Functional Dependencies & Normalization- 1 - Question 8

If a relation scheme is in BCNF, then it is also in

A.
First normal form
B.
Second normal form
C.
Third normal form
D.
All of the above

Detailed Solution: Question 8

BCNF is the more restrictive compared to 3NF. 3NF is more restrictive as compared to 2NF and so on.
Hence option (d) is correct.

Test: Functional Dependencies & Normalization- 1 - Question 9

For relation R(A, B, C, D, E, F) the set of FD’s is {A → C, B → D, C → E, D → E, E → A, F → B} What is the candidate key for R?

A.
A
B.
C
C.
D
D.
F

Detailed Solution: Question 9

According to the given set of functional dependencies

Test: Functional Dependencies & Normalization- 1 - Question 10

A set of FDs is given for a relation R (A, B, C, D, E, F, G)

What is the closure of {A, C}⁺ under this set?

A.
A, B, C
B.
A, B, C, D
C.
A, B, C, D, E, F
D.
A, B, C, D, E

Detailed Solution: Question 10

Hence (d) is the correct option.

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GATE Computer Science Engineering(CSE) 2027 Test: Functional Dependencies

MCQ Practice Test & Solutions: Test: Functional Dependencies & Normalization- 1 (10 Questions)

Which normal form is considered adequate for relational database design?

If every non-key attribute is functionally dependent on the primary key, then the relation will be in

Given the functional dependencies:
X→W; X→Y; Y→Z and Z→PQ
Which of the following does not hold good?

For a database relation R(a, b, c, d) where the domains of a, b, c and d include only atomic values, only the following functional dependencies and those that can be inferred from them hold.
a → c
b→d
The relation is in

Third normal form is inadequate in situations where the relation

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance.
Q. Which is the discriminator of the weak entity?

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance.
Q. Which is the primary key of the weak entity?

If a relation scheme is in BCNF, then it is also in

For relation R(A, B, C, D, E, F) the set of FD’s is {A → C, B → D, C → E, D → E, E → A, F → B} What is the candidate key for R?

A set of FDs is given for a relation R (A, B, C, D, E, F, G)

What is the closure of {A, C}⁺ under this set?

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GATE Computer Science Engineering(CSE) 2027 Test: Functional Dependencies

MCQ Practice Test & Solutions: Test: Functional Dependencies & Normalization- 1 (10 Questions)

Which normal form is considered adequate for relational database design?

If every non-key attribute is functionally dependent on the primary key, then the relation will be in

Given the functional dependencies: X→W; X→Y; Y→Z and Z→PQ Which of the following does not hold good?

For a database relation R(a, b, c, d) where the domains of a, b, c and d include only atomic values, only the following functional dependencies and those that can be inferred from them hold. a → c b→d The relation is in

Third normal form is inadequate in situations where the relation

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance. Q. Which is the discriminator of the weak entity?

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance. Q. Which is the primary key of the weak entity?

If a relation scheme is in BCNF, then it is also in

For relation R(A, B, C, D, E, F) the set of FD’s is {A → C, B → D, C → E, D → E, E → A, F → B} What is the candidate key for R?

A set of FDs is given for a relation R (A, B, C, D, E, F, G) What is the closure of {A, C}+ under this set?

GATE Computer Science Engineering(CSE) 2027 Mock Test Series

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Top Courses for Computer Science Engineering (CSE)

About this Computer Science Engineering (CSE) Practice Test

Explore more Computer Science Engineering (CSE) Study Resources

Given the functional dependencies:
X→W; X→Y; Y→Z and Z→PQ
Which of the following does not hold good?

For a database relation R(a, b, c, d) where the domains of a, b, c and d include only atomic values, only the following functional dependencies and those that can be inferred from them hold.
a → c
b→d
The relation is in

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance.
Q. Which is the discriminator of the weak entity?

Entity set TRANSACTION has the attributes transaction number, date, amount. Entity set ACCOUNT has the attributes account number, customer name, balance.
Q. Which is the primary key of the weak entity?

A set of FDs is given for a relation R (A, B, C, D, E, F, G)

What is the closure of {A, C}⁺ under this set?