relational-algebra

Definition

Relational Division (Relational Algebra)

The relational division operation, denoted by , is typically used to answer queries that involve the phrase “for all”. It finds all tuples in one relation that are associated with every single tuple from another relation .

The division operation can be expressed using projection, difference, and the Cartesian Product:


Explanation

removes all attributes from that are also attributes in .

combines all (-)-tuples with all -tuples.

yields the missing tuples that are not contained in .

yields the tuples of candidates that are missing combinations, from which the attributes of have been removed.

removes all candidates that were found to have missing tuples .

Therefore: removes all candidate tuples for which a required combination with exists that does not itself occur in .