1.Introduction
Relational database design theory is mainly based on a class of constraints called Functional Dependencies (FDs).FDs are a generalization of keys. This theory defines when a relation is in normal form (e.g., in Third Normal Form or 3NF) for a given set of FDs. It is usually a sign of bad DB design if a schema contains relations that violate the normal form requirements. If a normal form is violated, data is stored redundantly, and information about different concepts is intermixed. To reduce the redundancy in a given relation we need to decompose it in two or more sub relations .
Decomposition into highest normal forms required maintaining properties like loss less join decomposition and dependency preserving decomposition. To normalize a relation R we have to remove certain dependencies that exist in it like partial dependency& transitive dependency.

Basic definitions

1.1 Functional dependency:
In a given table, an attribute Y is said to have a functional dependency on a set of attributes X (written X → Y) if and only if each X value is associated with precisely one Y value. For example, in an "Employee" table that includes the attributes "Employee ID" and "Employee Date of Birth", the functional dependency {Employee ID} → {Employee Date of Birth} would hold. It follows from the previous two sentences that each {Employee ID} is associated with precisely one {Employee Date of Birth}.

1.2 Trivial functional dependency
A trivial functional dependency is a functional dependency of an attribute on a superset of itself. {Employee ID, Employee Address} → {Employee Address} is trivial, as is {Employee Address} → {Employee Address}.

1.3 Full functional dependency
An attribute is fully functionally dependent on a set of attributes X if it is: functionally dependent on X, and not functionally dependent on any proper subset of X. {Employee