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In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, Other notations for the converse relation include or

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rdfs:label	Umkehrrelation (de) Inversa rilato (eo) Relación inversa (es) Converse relation (en) Relation inverse (fr) 逆関係 (ja) Relacja odwrotna (pl) Relação inversa (pt) Обернене відношення (uk)
rdfs:comment	En logiko kaj matematiko, la inversa rilato de duargumenta rilato estas la duargumenta rilato difinita per . La inversa rilato estas ankaŭ nomita la rea rilato kaj povas esti skribita kiel , aŭ . Aparte, la inversa rilato de funkcio estas la duargumenta rilato difinita per . Ne bezone la inversa rilato de funkcio estas mem funkcio. En la okazo ke ĝi estas funkcio, ĝi nomiĝas kiel la de la fonta funkcio. (eo) Une relation inverse est une relation mathématique dans laquelle une des deux variables décroît lorsque l'autre augmente. Cette notion s'oppose à celle de relation directe. * Portail des mathématiques (fr) 数学における二項関係の逆関係（ぎゃくかんけい、英: converse relation）は、関係（のグラフ）に属する順序対の成分を逆順にして得られる関係である。例えば、「～の子である」という関係の逆関係は「～の親である」という関係である。 (ja) Relacja odwrotna do pewnej relacji binarnej to relacja powstała przez zmianę kolejności jej argumentów. (pl) Analogamente ao conceito de função inversa, podemos definir a relação inversa da relação : Note-se que nem sempre (aliás, quase nunca) . (pt) Обернене відношення — в математиці це бінарне відношення, взяте в зворотному порядку по відношенню до даного. (uk) In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, Other notations for the converse relation include or (en) En matemáticas, la relación inversa o transposición de una relación binaria es la relación que aparece cuando el orden de los elementos es intercambiado en la relación. Por ejemplo, la inversa de la relación «hijo de» es la relación «padre de». En términos formales, si X e Y son conjuntos y L ⊆ X × Y es una relación de X en Y, entonces LT es la relación definida tal que y LT x si y solo si x L y. En notación de constructor de conjuntos, LT = {(y, x) ∈ Y × X \| (x, y) ∈ L}. Otras notaciones para la relación inversa son LC, L–1, L~, , L°, o L∨. (es)
dct:subject	Binary relations Mathematical logic
Wikipage page ID	3941020 (xsd:integer)
Wikipage revision ID	1120992004 (xsd:integer)
Link from a Wikipage to another Wikipage	Binary relation Dagger category Unary operation Universe (mathematics) Connected relation Mathematics Quantale Endorelation Function (mathematics) Monoid Antisymmetric relation Sibling Bijective Composition of relations Partial function Total order Transitive relation Transpose Logical matrix Algebraic logic Equivalence relation Asymmetric relation Inverse function Involution (mathematics) Irreflexive relation Surjective Binary relations Mathematical logic Binary operation Supremum Symmetric relation Identity relation Aunt Identity function If and only if Nephew and niece Category (mathematics) Category of relations Reflexive relation Set (mathematics) Kinship Uncle Naive Set Theory (book) Heterogeneous relation Semigroup with involution Set-builder notation Partial order Injective Self-adjoint Order relation Transpose matrix Strict weak order Set membership Multi-valued
Link from a Wikipage to an external page	https://archive.org/details/naivesettheory0000halm_r4g0/page/40
sameAs	Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation Converse relation
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has abstract	En logiko kaj matematiko, la inversa rilato de duargumenta rilato estas la duargumenta rilato difinita per . La inversa rilato estas ankaŭ nomita la rea rilato kaj povas esti skribita kiel , aŭ . Aparte, la inversa rilato de funkcio estas la duargumenta rilato difinita per . Ne bezone la inversa rilato de funkcio estas mem funkcio. En la okazo ke ĝi estas funkcio, ĝi nomiĝas kiel la de la fonta funkcio. (eo) In mathematics, the converse relation, or transpose, of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if and are sets and is a relation from to then is the relation defined so that if and only if In set-builder notation, The notation is analogous with that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse. The unary operation that maps a relation to the converse relation is an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or, more generally, induces a dagger category on the category of relations as . As a unary operation, taking the converse (sometimes called conversion or transposition) commutes with the order-related operations of the calculus of relations, that is it commutes with union, intersection, and complement. Since a relation may be represented by a logical matrix, and the logical matrix of the converse relation is the transpose of the original, the converse relation is also called the transpose relation. It has also been called the opposite or dual of the original relation, or the inverse of the original relation, or the reciprocal of the relation Other notations for the converse relation include or (en)

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