If every Attribute of R is Prime Attribute then

Question

R always in "3NF" but "may not BCNF"

T/F and why?

Comments

in this case let suppose you have functional dependency of type

left side --> right side , so think if every attribute is prime attribute then does this happen that right side of dependency is "non prime" ? it can't happen so eventually right side will always have prime attributes so this make it 3NF , but then BCNF ? can you say left side would always be Super Key ?  No you can't say. so 3NF but not BCNF.

Answer 1

It took me a minute to come to conclusion but statement is TRUE because

consider this : AB -> CD

                           AC->BD

                          D -> A

prime attribute:{ A,B,C,D} // Since candidate keys are AB, AC, CD

All attributes here are prime!! 

​​​​​​but due to D->A table is in 3NF but not BCNF since 'D' is proper subset of candidate key not the super key. 

Answer 2

If a relation is in BCNF , it will definately also in 3NF, however reverse is not true as BCNF is not subset of 3NF

Answer 3

As per the definition of BCNF says that LHS should be Super key and RHS could be anything, but they mentioned that R have only prime attributes, So in BCNF prime attribute need not be Super key or determined all the attributes of the relation. It could be 3 NF but can't in BCNF.

Answer 4

the answer is true

rules for 3NF:

for a non-trivial dependency x --> y on a relation R

1)x is a super key

2)or y is a prime attribute

rules for BCNF

for a non-trivial dependency x --> y on a relation R

x must be a super key

from thsi we can conclude that BCNF is a subset  of 3NF

thus every BCNF is in 3NF, but every 3NF may not be BCNF,

because if a 3Nf just satisfies the 2nd rule it will not be in BCNF