Examine the statement with example: "Functional dependencies help to identify repetition in a relation."

Functional dependencies in a database refer to the relationship between two sets of attributes. They help to identify repetition in a relation by ensuring that the data is logically represented and redundancy is minimized.

Let's break this down with an example:

Consider a relation, Student, with attributes Student_ID, Student_Name, and Student_Course.

Student_ID -> Student_Name, Student_Course

This functional dependency indicates that a Student_ID determines a Student_Name and a Student_Course. In other words, for each Student_ID, there is precisely one Student_Name and one Student_Course associated with it.

Now, let's say we have the following data:

1. (101, "John", "Math")
2. (102, "Mary", "English")
3. (101, "John", "Science")

In this case, the Student_ID '101' is associated with the same Student_Name 'John' but different Student_Course. This is a repetition of the Student_Name for the same Student_ID, which is not efficient and can lead to inconsistencies.

Functional dependencies help to identify such repetitions. By normalizing the relation based on functional dependencies, we can eliminate these repetitions. In this case, we can split the relation into two:

1. Student(Student_ID, Student_Name)
2. Enrollment(Student_ID, Student_Course)

Now, the data would look like this:

Student:

1. (101, "John")
2. (102, "Mary")

Enrollment:

1. (101, "Math")
2. (102, "English")
3. (101, "Science")

This way, the repetition of 'John' for Student_ID '101' is eliminated. This is how functional dependencies help to identify and remove repetition in a relation.