Define Functonal dependencies. Explain trival and non trival dependencies?

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Functional dependency is a set of constraints between two attributes in a relation. Functional dependency says that if two tuples have the same values for attributes A1, A2,…, An, then those two tuples must have to have same values for attributes B1, B2, …, Bn.

Functional dependency is represented by an arrow sign (→) that is, X→Y, where X functionally determines Y. The left-hand side attributes determine the values of attributes on the right-hand side.

Trival Functional Dependency:

In Trivial Functional Dependency, a dependent is always a subset of the determinant.

i.e. If X → Y and Y is the subset of X, then it is called trivial functional dependency

For example:

roll_no name age
42 abc 17
43 pqr 18
44 xyz 18

Here, {roll_no, name} → name is a trivial functional dependency since the dependent name is a subset of determinant set {roll_no, name}

Similarly, roll_no → roll_no is also an example of trivial functional dependency.

Non-Trivial Functional Dependency:

In Non-trivial functional dependency, the dependent is strictly not a subset of the determinant.

i.e. If X → Y and Y are not a subset of X, then it is called Non-trivial functional dependency.

For example,

roll_no name age
42 abc 17
43 pqr 18
44 xyz 18

Here, roll_no → name is a non-trivial functional dependency, since the dependent name is not a subset of determinant roll_no

Similarly, {roll_no, name} → age is also a non-trivial functional dependency, since age is not a subset of {roll_no, name} 

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