Functional Dependencies

Rules of Functional Dependencies

• Reflexive rule :. If A is a set of attributes and B is subset of A, then A holds a value of B.
• Augmentation rule : When A -> B holds, and C is attribute set, then AC->BC also holds. That is adding attributes which do not change the basic dependencies.
• Transitivity rule : This rule is very much similar to the transitive rule in algebra if A->B holds and B->C holds, then A->C also holds. A->B is called as functionally that determines B.

Multivalued Dependency

• Multivalued dependency occurs in the situation where there are multiple independent multivalued attributes in a single table.
• A multivalued dependency is a complete constraint between two sets of attributes in a relation.

Example:

• In this example, Manufacture_year and colour are independent of each other but dependent on Car_model. In this example, these two columns are said to be multivalue dependent on Car_model.
• This dependence can be represented like this:
  • Car_model -> Manufacture_year
  • Car_model-> colour

Trivial Functional dependency

• The Trivial dependency is a set of attributes which are called a trivial if the set of attributes are included in that attribute.
• A->B is a trivial functional dependency if B is a subset of A.

Example:

In the above table,{Stu_ID, Stu_Name} -> Stu_ID is a trivial functional dependency as Stu_ID is a subset of {Stu_ID,Stu_Name}.

Non trivial functional dependency

• In a relationship, if attribute B is not a subset of attribute A, then it is considered as a non-trivial dependency.
• A nontrivial dependency occurs when A->B holds true where B is not a subset of A.

Example:

• {Stu_ID} -> {Stu_Name} (if we know the Stu_ID, we knows the Stu_Name)
• But Stu_Name is not a subset of Stu_ID, and hence it’s non-trivial functional dependency.

Transitive dependency

A transitive is a type of functional dependency which happens when it is indirectly formed by two functional dependencies.

Example:

• {Stu_ID} -> {Stu_Name} (if we know the Stu_ID, we know its Stu_Name)
• {Stu_Name} -> {Marks} If we know the Stu_Name, we know the Marks
• Therefore according to the rule transitive dependency: {Stu_ID} -> {Marks} should hold, that makes sense because if we know the Stu_ID, we can know his/her marks.

Advantages of Functional Dependency

• Functional Dependency avoids data redundancy. Therefore same data do not repeat at multiple locations in that database
• It helps you to maintain the quality of data in the database
• It helps you to define meanings and constraints of databases
• It helps you to identify bad designs
• It helps you to find the facts regarding the database design