db

Question

Assume 2 relational schemas R1(ABCDEF) and R2(ABC) with following FD’s
{AB→C,C→ABDE,DAE→F}
Which of the following statements is true?

1.   Both R1 and R2 are in BCNF
2.   Both R1 and R2 are in 3NF only
3.  ​​​​​​​ R1 is in 2NF and R2 in 3NF
4.    Both R1 and R2 are in 2NF only

Comments

is A subset of some candidate key? post the complete question if possible

---

no, i think DAE-->F is not partial dependency. LHS is not subset of candidate key.
partial dependency shud contain non-prime attribute depending on part of CK. but here F is not dependent on A alone.

---

according to me R1 is in 3nf, R2 in BCNF

Answer 1

Option 3 is correct

in R1(ABCDEF)

FDs are

AB->C

C->ABDE

DAE->F

in R1 candidate key are {AB,C}

so there is no partial dependency so it is 2NF

it can't be in 3NF due to DAE->F

 

in R2(ABC)

FDs

AB->C

and AB is key

so it is in 3NF

Comments

DAE->F

'A' prime attribute and part of the candidate key and 'F' non-prime attribute. Is it not the partial dependency?

---

A functional dependency X → Y is a full functional dependency if removal of any attribute A from X means that the dependency does not hold any more; that is, for any attribute A ε X, (X – {A}) does not functionally determine Y.

 

A functional dependency X → Y is a partial dependency if some attribute A ε X can be removed from X and the dependency still holds; that is, for some A ε X, (X – {A}) → Y.

 

The definition of 2NF involves full functional dependency of non-key attributes on keys but any functional dependecy that holds is either full or partial.

-- FUNDAMENTALS OF Database Systems SIXTH EDITION Ramez Elmasri & Navathe