Consider the following set of functional dependency on the schema (A, B,C)
A→BC, B→C, A→B, AB→C
The canonical cover for this set is:
a)
A->BC and B->C
b)
A->BC and AB->C
c)
A->BC and A->B
d)
A->B and B->C
Correct answer is option 'A'. Can you explain this answer?

Question

Consider the following set of functional dependency on the schema (A, B,C)
A→BC, B→C, A→B, AB→C
The canonical cover for this set is:

a)
A->BC and B->C
b)
A->BC and AB->C
c)
A->BC and A->B
d)
A->B and B->C

Correct answer is option 'A'. Can you explain this answer?

Answer

Understanding Functional Dependencies
Functional dependencies (FDs) are crucial in database design, helping to minimize redundancy. The given FDs for the schema (A, B, C) are:
- A → BC
- B → C
- A → B
- AB → C
What is a Canonical Cover?
A canonical cover (or minimal cover) is a simplified set of FDs that preserves the original dependencies but removes redundancies. It should be minimal in terms of both left-hand sides and the set of FDs.
Steps to Find the Canonical Cover
1. Remove Extraneous Attributes:
- For A → BC, neither A nor any attribute can be removed since both are necessary.
- For B → C, B is essential.
- For A → B, A is also necessary.
- For AB → C, A and B are both required.
2. Remove Redundant Dependencies:
- We check if any FD can be derived from others:
- From A → B and A → BC, we can derive A → C (since A → B implies A → C using B → C).
- Hence, A → BC can be kept, while AB → C becomes redundant.
3. Finalizing the Canonical Cover:
- The remaining FDs after simplification are:
- A → BC
- B → C
- A → B
Conclusion: The Canonical Cover
Hence, the minimal representation, which preserves all functional dependencies without redundancy, is:
- A → BC
- B → C
Thus, the correct answer is option 'A': A → BC and B → C.

Answer

All of the FDs are implied by the FDs {A->BC, B->C}
From option b: A⁺= BC (hence A->BC, A->b and AB->Care implied by FDs set given in option b)
B⁺= BC (hence B->C is implied by FDs set given in option b)

Similar Computer Science Engineering (CSE) Doubts

Consider the following set of functional dependency on the schema (A, B,C)A→BC, B→C, A→B, AB→CThe canonical cover for this set is

Consider the following set offunctional dependencies on the scheme (A, B, C).A —> BC, B —> C, A —> B ,A B —> CThe canonical cover for this set is

What is the canonical cover of the following set F of functional dependencies on the schema(A, B,C)?A → BCB → CA → BAB → C

What is the canonical cover of the following set F of functional dependencies on the schema (A, B,C)?A → BCB → CA → BAB → C

Consider the following set of functional dependencies F on the schema S(P, Q, R)F = {P → QR, PQ → R, Q → R, P → Q}The canonical cover of the above given set is

Top Courses for Computer Science Engineering (CSE)View all

GATE Computer Science Engineering(CSE) 2025 Mock Test Series

Question Bank for GATE Computer Science Engineering

General Aptitude for GATE

Computer Networks

Programming and Data Structures

Top Courses for Computer Science Engineering (CSE)

Top Courses for Computer Science Engineering (CSE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company