BE - Database Management Systems

The division operator (÷) in relational algebra is used to answer queries that involve the phrase “for all”.
It is particularly useful when we want to find entities (like students, suppliers, etc.) that are related to all values of another set.

Division Operator Used

• Division queries are used when we are asking about entities that are associated with every element of another set.

• Typical use cases:

  • Find students who have taken all courses.

  • Find suppliers who supply all parts.

  • Find employees who are working on all projects.

Formal Definition

Suppose we have two relations:

• R(A,B)

• S(B)

The result of R÷S is a relation T(A) such that:

• $T$ contains all values of A from relation R that are associated with every value of B in relation S.

The division operator is used for queries involving “for all” conditions. It retrieves tuples from one relation that are related to all tuples of another relation. Common use cases are "students who took all courses," "suppliers who supply all parts," or "employees working on all projects."