GATE Exam > GATE Questions > Consider the following relation R(A, B, C, D...
Start Learning for Free
Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.
F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}
Which of the following is the minimal cover of F?
- a){BC → A, BC → E, A → F, C → D, A → G}
- b){BC → A, B → E, A → F, F → G, C → D}
- c){BC → A, BC → E, A → F, F → G, C → D}
- d){BC → A, BC → E, A → F, C → D}
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Consider the following relation R(A, B, C, D, E, F, G) and set of fun...
(1) RHS contain single attribute
A → F …..(1)
F → G …..(2)
A → G …….(3)
Hence FD' (3) is redundant.
Now consider
BCD → A
(BC)+ = BCEDAFG
It contains attribute D, D is redundant.
Minimal cover is {BC → A, BC → E, A → F, F → G, C → D}
So option (c) is correct.
Most Upvoted Answer
Consider the following relation R(A, B, C, D, E, F, G) and set of fun...
To find the minimal cover of a set of functional dependencies, we need to simplify the set by removing redundant or extraneous dependencies. Here is the step-by-step process to find the minimal cover of the given set of functional dependencies F:
1. Decompose the right-hand side of each dependency in F:
- BCD → A can be decomposed as BCD → A and BCD → C and BCD → D
- BC → E can be decomposed as BC → E
- A → F can be decomposed as A → F
- F → G can be decomposed as F → G
- C → D can be decomposed as C → D
- A → G can be decomposed as A → G
2. Remove extraneous attributes from the left-hand side of each dependency. If any attribute can be removed without changing the closure of the left-hand side, it is extraneous. Repeat this process until no more extraneous attributes can be removed.
- BCD → A remains the same
- BC → E remains the same
- A → F remains the same
- F → G remains the same
- C → D remains the same
- A → G remains the same
3. Remove redundant dependencies. If any dependency can be derived from the remaining dependencies, it is redundant and can be removed.
- BCD → A remains the same
- BC → E remains the same
- A → F remains the same
- F → G remains the same
- C → D remains the same
- A → G remains the same
4. Combine dependencies with the same left-hand side.
- BCD → A remains the same
- BC → E remains the same
- A → F remains the same
- F → G remains the same
- C → D remains the same
- A → G remains the same
5. The resulting set is the minimal cover of F:
- {BCD → A, BC → E, A → F, F → G, C → D, A → G}
Therefore, the correct answer is option C: {BCD → A, BC → E, A → F, F → G, C → D}.
1. Decompose the right-hand side of each dependency in F:
- BCD → A can be decomposed as BCD → A and BCD → C and BCD → D
- BC → E can be decomposed as BC → E
- A → F can be decomposed as A → F
- F → G can be decomposed as F → G
- C → D can be decomposed as C → D
- A → G can be decomposed as A → G
2. Remove extraneous attributes from the left-hand side of each dependency. If any attribute can be removed without changing the closure of the left-hand side, it is extraneous. Repeat this process until no more extraneous attributes can be removed.
- BCD → A remains the same
- BC → E remains the same
- A → F remains the same
- F → G remains the same
- C → D remains the same
- A → G remains the same
3. Remove redundant dependencies. If any dependency can be derived from the remaining dependencies, it is redundant and can be removed.
- BCD → A remains the same
- BC → E remains the same
- A → F remains the same
- F → G remains the same
- C → D remains the same
- A → G remains the same
4. Combine dependencies with the same left-hand side.
- BCD → A remains the same
- BC → E remains the same
- A → F remains the same
- F → G remains the same
- C → D remains the same
- A → G remains the same
5. The resulting set is the minimal cover of F:
- {BCD → A, BC → E, A → F, F → G, C → D, A → G}
Therefore, the correct answer is option C: {BCD → A, BC → E, A → F, F → G, C → D}.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer?
Question Description
Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer?.
Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer?.
Solutions for Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following relation R(A, B, C, D, E, F, G) and set of functional dependencies.F = {BCD → A, BC → E, A → F, F → G, C → D, A → G}Which of the following is the minimal cover of F?a){BC → A, BC → E, A → F, C → D, A → G}b){BC → A, B → E, A → F, F → G, C → D}c){BC → A, BC → E, A → F, F → G, C → D}d){BC → A, BC → E, A → F, C → D}Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup