F+ is called as the closure of F. It contains all the possible combinations of a functional dependency set in it.

X→ Y is said to be trivial if X is a subset of Y. Thus X ⊂ Y implies X→Y is trivial.

A relation that satisfies all the real world constraints is called as a legal relation. An instance of a legal relation is called as a legal instance.

The fourth normal form exists and is different from the Boyce Codd normal form which is called as BCNF.

Each attribute in X-Y is a candidate key for R is not a necessary condition for the third normal form in the case of X → Y. X→Y is trivial and X is the superkey of R are necessary conditions for the third normal form.

Y does not need to be a superkey of the relation for the given functional dependency to satisfy BCNF. X→ Y must be trivial and X must be the superkey of the relation R.

If K → R then k is said to be the superkey of R i.e. K uniquely identifies every tuple in the relation R.

A functional dependency must first satisfy the second normal form to satisfy the third normal form. The second normal form must in turn satisfy first normal form.

Primary keys, Functional dependencies, Check clause are all used to express database consistency.

X → Y holds on a schema k(K) if each and every legal instance satisfies the functional dependency. Even if one instance does not satisfy the functional dependency X→ Y does not hold on a schema.