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Commutative Associative Binary Operations on a Set with Three Elements

Yogesh Kumar Sarita

Associativity, Commutative, Existence of identity are fundamental properties of binary operation in abstract algebra. In this paper, the authors discuss binary operations on a three-element set and show, by partition and composition of mapping, that exactly 63 operations out of the 19683 existing binary operations on the set are associative as well as commutative with counting that how many composition tables are to be verified