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Course Queries Syllabus Queries 2 years ago
Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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I am not sure whether this is offtopic. However, please read on.
A person whom I know has encountered a problem in the answer key published by CBSE, India. As their key challenging form contains a column for citation/proof, we have to find some authentic book which can be shown as the base of our claim.
I attach the question here, and I request you to verify the answer and suggest us some book/other ways to prove our challenge (She has checked the regular syllabus books, but didn't find something precise related to this problem).
Question:
Identify the minimal key for relational scheme R(A, B, C, D, E) with functional dependencies F = {A->B, B->C, AC->D}
The options are A, AE, BE, and CE
The key shows the answer is A and she says it is AE actually.
Please help us find some proof/way to challenge the key.
The key is actually AE. The proof is simple, a key for definition is a minimal set of attributes whose closure contains all the attributes of the table. If you calculate the closure of A with respect to the given functional dependencies you will find:
AE
A
A+ = {ABCD}
that does not contain the attribute E. So A is not a key, and E must be present in any key of R. And since:
E
R
AE+ = {ABCDE}
then AE is a key, and it is minimal (you cannot remove any attribute from it without losing the property of determining all the other attributes of the relation).
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