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Consider the schema R = (A, B, C, D, E, F) on which the following functional dependencies hold:
A ➝ B
B, C ➝ D
E ➝ C
D ➝ A
What are the candidate keys of R?
  • a)
    AEF, BEF and DEF
  • b)
    AEF, BEF and BCF
  • c)
    AE and BE
  • d)
    AE, BE and DE
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider the schema R = (A, B, C, D, E, F) on which the following func...
Concept:
Candidate key: it is the set of attributes which uniquely identifies a relation. It is also known as superkey with no repeated attributes.
Given relation R = {A, B, C, D, E}
A ➝ B
B, C ➝ D
E ➝ C
D ➝ A
Find the closure of keys given. If all the attributes of relation are present in the closure, then it will be the candidate key of that relation.
Option1: AEF, BEF and DEF
(AEF)+ = {A, E, F, B, C, D}
(BEF)+ = {B, E, F, C, D, A}
(DEF)+ = {D, E, F, C, A, B}
These are the candidate keys of given relation.
Option2: AEF, BEF and BCF
(AEF)+ = {A, E, F, B, C, D}
(BEF)+ = {B, E, F, C, D, A}
(BCF)+ = {B, C, F, D, A}  // E is not present in the closure. Not the candidate key
Option3: AE and BE
(AE)+ = {A, E, C, B, D, }  //F is not present, not a candidate key
(BE)+ = {B, E, C, D, A}   //F is not present, not a candidate key
Option4: AE, BE and DE
(AE)+ = {A, E, C, B, D, } //F is not present, not a candidate key
(BE)+ = {B, E, C, D, A}  //F is not present, not a candidate key
(DE)+ = {D, E, A, C, B}   //F is not present, not a candidate key
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Consider the schema R = (A, B, C, D, E, F) on which the following functional dependencies hold:A ➝ BB, C ➝ DE ➝ CD ➝ AWhat are the candidate keys of R?a)AEF, BEF and DEFb)AEF, BEF and BCFc)AE and BEd)AE, BE and DECorrect answer is option 'A'. Can you explain this answer?
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