In mathematics and abstract algebra, a "'relation algebra "'is a residuated Boolean algebra composition of binary relations " R " and " S ", and with the converse of " R " interpreted as the inverse relation.
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This technique works for example 2 because subalgebras and direct products of algebras of binary relations are themselves algebras of binary relations, showing that the class "'RRA "'of representable relation algebras is a quasivariety ( and " a fortiori " an elementary class ).
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The "'representable relation algebras "', forming the class "'RRA "', are those relation algebras isomorphic to some relation algebra consisting of binary relations on some set, and closed under the intended interpretation of the "'RA "'operations.
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The "'representable relation algebras "', forming the class "'RRA "', are those relation algebras isomorphic to some relation algebra consisting of binary relations on some set, and closed under the intended interpretation of the "'RA "'operations.
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The "'representable relation algebras "', forming the class "'RRA "', are those relation algebras isomorphic to some relation algebra consisting of binary relations on some set, and closed under the intended interpretation of the "'RA "'operations.
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That not every relation algebra is representable is a fundamental way "'RA "'differs from "'QRA "'and Boolean algebras, which, by Stone's representation theorem for Boolean algebras, are always representable as sets of subsets of some set, closed under union, intersection, and complement.
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