trichotomy (Q54537198)

mathematical property for binary relations

Language	Label	Description	Also known as
English	trichotomy	mathematical property for binary relations	trichotomy property

Statements

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\forall x\in X\,\forall y\in X\,((x{\mathcal {R}}y\,\land \,\lnot (y{\mathcal {R}}x)\,\land \,\lnot (x=y)\,)\lor \,(\lnot (x{\mathcal {R}}y)\,\land \,y{\mathcal {R}}x\,\land \,\lnot (x=y)\,)\lor \,(\lnot (x{\mathcal {R}}y)\,\land \,\lnot (y{\mathcal {R}}x)\,\land \,x=y\,\,))

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