The three main classes of binary relations that exhibit closure operations are reflexive, transitive, and symmetric classes. From the intersection of these classes we get some other classes of relations that exhbit closure operations:
Preorder: reflexive and transitive
Dependency relation: reflexive and symmetric
Equivalence relation: reflexive, symmetric, and transitive
Another class of relation that exhibits a closure operation is the set of complete relations. Its corresponding closure operation is complete closure.
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