Editing Relational algebra (section)

==== Selection and set operators ====
Selection is [[distributive property|distributive]] over the set difference, intersection, and union operators.  The following three rules are used to push selection below set operations in the expression tree. For the set difference and the intersection operators, it is possible to apply the selection operator to just one of the operands following the transformation. This can be beneficial where one of the operands is small, and the overhead of evaluating the selection operator outweighs the benefits of using a smaller [[relation (database)|relation]] as an operand.

#<math>\sigma_{A}(R\setminus P)=\sigma_{A}(R)\setminus \sigma_{A}(P) =\sigma_{A}(R)\setminus P</math>
#<math>\sigma_{A}(R\cup P)=\sigma_{A}(R)\cup\sigma_{A}(P)</math>
#<math>\sigma_{A}(R\cap P)=\sigma_{A}(R)\cap\sigma_{A}(P)=\sigma_{A}(R)\cap P=R\cap \sigma_{A}(P)</math>