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 .