Abstract
The effects of five basic operations (asymmetrization, complementation, dualization, symmetrization, transitive closure) on binary relations are examined. Identifies between compound operations are developed (e.g. the symmetric part of the transitive closure of the complement of the transitive closure equals the transitive closure of the symmetric complement of the transitive closure), ordering aspects of compound operations are noted, and it is shown that in addition to the empty and universal relations at most 110 different relations can be generated from a given binary relation by sequential applications of the five basic operations. Moreover, 110 is the least upper bound, and none of these 110 requires more than seven applications of the basic operations for its expression. One of the potentially irreducible compound operations of length seven is cstcatc, the complement of the symmetric part of the transitive closure of the complement of the asymmetric part of the transitive closure of the complement.
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