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Which of the following is false when R is is in 3NF but not in BCNF

a)R must contain at least two overlapped CK

b)R must consist proper subset of CK determines proper subset of some other CK

c)R must consist  at most one compound CK and others are simple CK

d)R must consists at most two compound CK

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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}.

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}

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}.

We get Candidate keys = {AB, BD}  and Prime Attributes = A, B, D

  1. R must contain at least two overlapped CK – This is True. 
  2. 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.
  3. R must consist  at most one compound CK and others are simple CK – This is false. 
  4. R must consists at most two compound CK – This is also false. 

Therefore, Option C and D are false.

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