Closure is a set of functional dependencies that can denote F and certain other functional dependencies that are logically implied by set F of functional dependencies that can denote F+. F+ is a superset of F. Set is said to be closed under some operation when performance of that operation on Relational set and produces new Relational set. Axioms are helps to generate Functional Dependencies and individually process particular set through Closure and then produce a new Relation of the set.
An instance, an Employee Relational Entity can process with condition and then produce a new Employee Relational Entity. Let "R (U) F+" or "Relation (Union) F+" is symbolize a relational scheme over the set of attributes U with a set of Functional Dependencies F+. Let "R (U)" is denote a relational scheme over the set of attributes U. A set is defined with X, Y, Z attributes that can determine Union like X U Y U Z or XYZ.
Procedure for Computing F+
F+ = F
repeat
for each functional dependency f in F+
apply reflexivity and augmentation rules on f
add the resulting functional dependencies to F+
for each pair of functional dependencies f1 and f2 in F+
if f1 and f2 can be combined using transitivity
then add the resulting functional dependency to F+