1 NF (Normal Form)

The domain of attribute must include only atomic (simple, indivisible) values.

2NF

A relation schema R is in 2NF if it is in 1NF and every non-prime attribute A in R is fully functionally dependent on primary key.

3NF

A relation schema R is in 3NF if it is in 2NF and for every FD X —>A either of the following is true

X is a Super-key of R.

A is a prime attribute of R.

In other words, if every non prime attribute is non-transitively dependent on primary key.

4NF

A relation schema R is said to be in 4NF if for every Multivalued dependency X—>Y that holds over R, one of following is true

X is subset or equal to (or) XY = R.

X is a super key.

5NF

A Relation schema R is said to be 5NF if for every join dependency {R1, R2, …, Rn} that holds R, one the following is true

Ri = R for some i.

The join dependency is implied by the set of FD, over R in which the left side is key of R.

BCNF (Boyce-Codd Normal Form)?

A relation schema R is in BCNF if it is in 3NF and satisfies an additional constraint that for every FD X—>A, X must be a candidate key.