Difference Between 3NF And BCNF in Tabular Form

S.NO.3NFBCNF
Full Form3rd Normal FormBoyce–Codd Normal Form
DefinitionA relation is in 3NF if it is in 2NF and no non-prime attribute transitively depends on the primary key. In other words, a relation R is in 3NF if for each functional dependency X ⟶ A in R at least one of the following conditions are met:

  • X is a key or superkey in R
  • A is a prime attribute in R
A relation R is in BCNF if it is in 3NF and for each functional dependency X ⟶ A in R, X is a key or superkey in R. In other words, the only difference between 3NF and BCNF is that in BCNF it is not present the second condition of the 3NF. This makes BCNF stricter than 3NF as any relation that is in BCNF will be in 3NF but not necessarily every relation that is in 3NF will be in BCNF.
ExampleGiven the following relation:

EMP_DEPT(firstName, employeeNumber, dateOfBirth, address, departmentNumber, departmentName)

An employee can only work in one department and each department has many   employees.The candidate key is employeeNumber.

Consider the following functional dependencies:

employeeNumber⟶firstName, dateOfBirth,address,departmentNumber.

departmentNumber⟶departmentName.

Given the definition above it is possible to conclude that the relation EMP_DEPT is not in 3NF because the second functional dependency does not meet any of the 2 conditions of the 3NF:

departmentNumber is not a key or superkey in EMP_DEPT

departmentName is not a prime attribute in EMP_DEPT

(Number, courseNumber)

A student can assist to many courses and in a course there can be many students.

The candidate keys are:

socialSecurityNumber, courseNumber

studentNumber, courseNumber

Consider the following functional dependencies:

studentNumber,

socialSecurityNumber

socialSecurityNumber⟶studentNumber

Given the definition above it is possible to conclude that STUDENT_COURSE is not in BCNF as at least student.
Number is not a key or super-key in STUDENT_COURSE.

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