Let's look at the situation where redundancies can creep in even though a table is in Boyce-Codd normal form. Let's take the student / instructor / course example used in that article, but change one of the initial assumptions.

Assume that the following is true for the tables below:

• Each instructor takes only one course
• Each course can have one or more instructors
• Each student can have several instructors per course (this is different to the previous example)
• Each student can take one or more courses

Student Course Instructor data, with several instructors per course

More data anomalies

The data is the same as before, except that Helen Ginwala is teaching science to Gerrie Jantjies as well as mathematics to Dingaan Fortune, and Dingaan Fortune is being taught by both Helen Ginwala and Kader Dlamini for mathematics.

The only possible key is a combination of all three attributes, as shown below. No other combination will uniquely identify a particular record.

Three attributes as key

But this still has some potentially anomalous behavior. The fact that Kader Dlamini teaches mathematics is still stored more than once, as is the fact that Dingaan Thobela takes mathematics. The real problem is that the table stores more than one kind of fact: that of student-to-course relationship, as well as that of a student-to-instructor relationship. You can avoid this, as always, by separating the data into two tables, as shown below:

Creating a table for the student to instructor relationship

Creating a table for the student to course relationship

This situation exists when you have multiple multivalued dependencies. A multivalued dependency exists between two attributes when, for each value of the first attribute, there are one or more associated values of the second attribute. For each value of student, there were many values of course. This is the first multivalued dependency. Then, for each value of student, there are one or more associated values of instructor. This is the second multivalued dependency.

Thus, a table is in 4th normal form if:

• it is in Boyce-Codd normal form
• it does not contain more than one multivalued dependency