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As far as I know, the definition of a functional dependency reads that, given the attributes X and Y, "each X value is associated with precisely one Y value". But then the author of the article that I read called this a "one-to-many" relationship. Isn't this really "one-to-one"..?

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I think that the FD can't be described as "One-to-one" relationships. In One-to-one relationships, the X value identifies a Y value and vice-versa. In FD this doesn't happen. In fact, the Y values can be shared from different tuples with the same X value.

Think to a simple table with only cities, states and nations (And don't care about the redundancy). We know that the state identifies one and one nation, but a single nations doesn't identify a single state.

So, generally X implies Y but Y doesn't imply X.

A last observation: an one-to-one relationship need that the tables involved in the relationship must have the same number of rows, in order to associate to every a one b and to associate to every b one a. In the textbook you'll find a lot of FD in which this doesn't happen.

So we can describe a FD as an association of a Y value to many (only sometimes one) X values. So it's called an one-to-many relationship.

  • Because X is on the left side of the FD relationship, shouldn't it be described as "many-to-one" then, given your explanation..? – Exander Jan 26 '15 at 10:35
  • Often I found many-to-one and one-to-many as synonymous in DB theory. For example, in Relationships in ER model, if the first entity has cardinality (1,1) or (1,N) it is called however "one-to-many relationship" – EagleOne Jan 26 '15 at 10:41
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This example illustrates the concept of functional dependency. The situation modelled is that of college students visiting one or more lectures in each of which they are assigned a teaching assistant (TA). Let's further assume that every student is in some semester and is identified by a unique integer ID.

StudentID   Semester    Lecture             TA
1234        6           Numerical Methods   Azhar
1201        4           Numerical Methods   Peter
1234        6           Visual Computing    Ahmed
1201        4           Numerical Methods   Peter
1201        4           Physics II          Simone

We notice that whenever two rows in this table feature the same StudentID, they also necessarily have the same Semester values. This basic fact can be expressed by a functional dependency:

StudentID → Semester.

Other nontrivial functional dependencies can be identified, for example:

{StudentID, Lecture} → TA
{StudentID, Lecture} → {TA, Semester}

The latter expresses the fact that the set {StudentID, Lecture} is a superkey of the relation.

  • From this example, I still don't understand why the functional dependency is called a "one-to-many" relationship. In your example, the StudentID always has only one and the same Semester that corresponds to it. Where's the "many" here..? Same for other dependencies. – Exander Jan 23 '15 at 13:06
  • Is this exact copy paste of ? – vijayp Jan 23 '15 at 14:08
  • The data also suggest a Semester → StudentID dependency but I doubt that would appear with actual data. – ypercubeᵀᴹ Jan 23 '15 at 14:32
  • Also: this table has 2 identical rows. That makes it a not good example. – ypercubeᵀᴹ Jan 23 '15 at 14:33

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