Classification of Dependencies in DBMS –
S.NO  Classification of Dependencies  Which Normal Form Remove these Dependencies 
1  Partial Dependencies  Second Normal Form (2NF) 
2  Transitive Dependencies  Third Normal Form (3NF) 
3  Multivalued Dependencies  Fourth Normal Form (4NF) 
4  Join Dependencies  Fifth Normal Form (5NF) 
5  Inclusion Dependency  (Dependencies among the Relations/Tables or Databases) 
Partial dependencies and Transitive Dependencies are types of Functional Dependencies.
Functional Dependency
A Functional dependency is a relationship between attributes.
For example, if we know the value of customer account number, we can obtain customer address, balance etc. By this, we say that customer address and balance is functionally dependent on customer account number.
In general terms, attribute Y(customer address and balance) is functionally dependent on the attribute X(customer account number), if the value of X determines the value of Y.
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Partial Functional Dependency –
A Functional Dependency in which one or more non key attributes are functionally depending on a part of the primary key is called partial functional dependency. or
where the determinant consists of key attributes, but not the entire primary key, and the determined consist of nonkey attributes.
For example, Consider a Relation R(A,B,C,D,E) having FD : AB → CDE where PK is AB. Then, { A → C; A → D; A → E; B → C; B → D; B → E } all are Partial Dependencies.
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Transitive Dependency –
Given a relation R(A,B,C) then dependency like A–>B, B–>C is a transitive dependency, since A–>C is implied .
In the above Fig 1, SSN > DMGRSSN is a transitive FD {since SSN > DNUMBER and DNUMBER > DMGRSSN hold} SSN > ENAME is nontransitive FD since there is no set of attributes X where SSN > X and X > ENAME.
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Multivalued Dependency
Consider a relation Faculty (FID, Course, Book) which consists of two multivalued attributes (Course and Book). The two multivalued attributes are independent of each other.

⇒ 

it is clear that there are multiple copies of the information about Course and Book. This is an example of a multivalued dependency which occurs when a relation has more than one independent, multivalued attribute.
A multivalued dependency occurs when a relation R has attributes A(FID), B(Course), and C(Book) such that
 A determines a set of values for B
 A determines a set of values for C and
 B and C are independent of each other. (No relation between Course and Book)
These multivalued dependencies can be indicated as follows :
 (FID → → Course)
 (FID → → Book)
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Join Dependency
Let R be a relation. Let A, B, …, Z be arbitrary subsets of R’s attributes. R satisfies the JD
* ( A, B, …, Z )
if and only if R is equal to the join of its projections on A, B, …, Z.
A join dependency JD(R1, R2, …, Rn) specified on relation schema R, is a trivial JD, if one of the relation schemas Ri in JD(R1, R2, ….,Rn) is equal to R.
Inclusion Dependencies
An inclusion dependency (shortly called as INDs) are the dependencies which exists when some columns of a relation are contained in other columns (usually of a second relation). The example of Inclusion dependency is a foreign key constraint or Referential Integrity Constraint as it states that the referring column(s) in one relation must be contained in the primary key column(s) of the referenced relation.
Objective of Inclusion Dependencies:
To formalize two types of interrelational constraints which cannot be expressed using F.D.s or MVDs:
 Referential integrity constraints
 Class/subclass relationships
Inclusion dependencies are mostly keybased, i.e. which involve only keys. Referential Integrity or Foreign key constraints are a good example of keybased inclusion dependencies. An ERD(er diagram) that involves ISA hierarchies also leads to keybased inclusion dependencies.
If all inclusion dependencies are keybased then we rarely have to worry about splitting attribute groups that participate in inclusions, since decompositions usually do not split the primary key.
Note that going from 3NF to BCNF always involves splitting some key, hopefully not the primary key, since the dependency guiding the split is of the form X → A where A is part of a key.
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