Difference

Synonyms

Set difference

Definition

The difference of two relation instances R₁ and R₂ over the same set of attributes U, denoted by R₁ − R₂, is another relation instance over U containing precisely the set of tuples occurring in R₁ and not occurring in R₂.

Key Points

The difference is one of the primitive operators of the relational algebra. It coincides with the notion of set difference, with the additional restriction that it can be applied only to relations over the same set of attributes. However the difference of two arbitrary relations having the same arity can be obtained by first renaming attributes in one of the two relations.

As an example, consider a relation Students over attributes (number, name), containing tuples {(1001, Black), (1002, White)}, and a relation Employees over attributes (number, name), containing tuples {(1001, Black), (1003, Brown)}. Then the difference Students − Employees is a relation over attributes (number, name) containing the only tuple (1002, White)....