Question

Given the following two statements:

S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF.

S2: AB → C, D → E, E → C is a minimal cover for the set of functional dependencies AB → C, D → E, AB → E, E → C.

Which one of the following is CORRECT?

1. S1 is TRUE and S2 is FALSE
2. Both S1 and S2 are TRUE.
3. S1 is FALSE and S2 is TRUE
4. Both S1 and S2 are FALSE

Answer 1

Correct Answer - Option 1 : S1 is TRUE and S2 is FALSE

Statement 1: TRUE

BCNF (Boyce Codd Normal Form):

• A relation R is in BCNF whenever a non – trivial functional dependency X → A holds in R, where X is the super-key of R.
• A binary relation is always in BCNF. A binary relation contains only two attributes.
• Functional dependency that is possible from a binary relation is one.

Example:

Consider R(A, B), in this only one functional dependency is possible either A → B or B → A

In both the cases, left hand side will be the super key. In this way R(A, B) is always in BCNF.

If a relation is in BCNF then it is in 1NF, 2 NF and 3 NF

Statement 2: FALSE

Set 1 = {AB → C, D → E, AB → E, E→ C}

Set 2 = {AB → C, D → E, E → C}

Set 2 cannot derive   AB → E since in set 2 (AB)⁺ = {A, B, C}

The two sets of functional dependencies are not the same and hence one cannot be minimal of other.