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?

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.