Understanding Trivial Functional Dependency

In a trivial functional dependency one attribute is a subset of another

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In the world of relational database theory, a functional dependency exists when one attribute determines another attribute uniquely in a database. A trivial functional dependency is a database dependency that occurs when describing a functional dependency of an attribute or of a collection of attributes that includes the original attribute. 

Examples of Trivial Functional Dependencies

This kind of dependency is called trivial because it can be derived from common sense.

If one "side" is a subset of the other, it's considered trivial. The left side is considered the determinant and the right the dependent.

  • {A,B} –> B is a trivial functional dependency because B is a subset of A,B. Since {A,B} –> B includes B, the value of B can be determined. It's a trivial functional dependency because determining B is satisfied by its relationship to A,B.  Since the values of B are determined by the values of A, any other sequence that shares the values of A will have the exact same values as B. Another way to put it is that all of B is included in A, which is why it is A's subset. 
  • {Employee_ID, Employee_Name} –> Employee_ID is also a trivial functional dependency since Employee_ID is a subset of {Employee_ID, Employee_Name}.
  • The same is true for A –> A or Employee_ID –> Employee_ID,  and Employee_Name –> Employee_Name. These are all trivial functional dependencies.
  • If a functional dependency X–>Y, and Y is a subset of X, this is a trivial functional dependency. If Y is not a subset of X, this is not a trivial functional dependency.
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