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3 Answers

11 votes
11 votes

no, if all attributes are prime then table is definitely in 3NF but we can't ensure BCNF 

for BCNF,

 every one of its dependencies X → Y, at least one of the following conditions hold:[2]

  • X → Y is a trivial functional dependency (Y ⊆ X)
  • X is a super key for schema R

even if all the attributes are part of any key attribute(prime-attribute)

there is chance that L.H.S of all the FD is not super key

let a relation R(ABCD)

ABC --> D  CD --> A

ABC and BCD are CK for this relation

but CD is not super key...A.B.C and D all are prime attributes still its not in BCNF

0 votes
0 votes
NO .

This will clear rule for the 3NF .

In BCNF all the left hand side of FDs will be superkeys .then we can surely be in BCNF.
0 votes
0 votes
Relation R(ABCDE) FD : { AB -> C, C->D , D->A}

Here A,B,C,D all are prime attribute and R in 3NF

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