Consider the following 3 examples which are in 3NF but not in BCNF.and validate the options
Ex1: R = {A, B, C, D, E} and F = {A -> B, B C - > E, E D -> A}
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We get Candidate keys = {ACD, BCD, CDE} and Prime Attributes = A, B, C ,D, E(all attributes)
Ex2: R(ABC) and F = {AB -> C, C - > B}
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We get Candidate keys = {AB,AC} and Prime Attributes = A, B, C (all attributes)
Ex3: R = {A, B, C, D, E} and F = {AB -> CDE, D -> A}
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We get Candidate keys = {AB, BD} and Prime Attributes = A, B, D
- R must contain at least two overlapped CK – This is True.
- R must consist proper subset of CK determines proper subset of some other CK- This is true. Every given FD is a proper subset of every other CK.
- R must consist at most one compound CK and others are simple CK – This is false.
- R must consists at most two compound CK – This is also false.
Therefore, Option C and D are false.