In mathematics, the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'.

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  • In mathematics, the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'. In formal terms, if <math>L : X \to Y</math> is a binary relation with <math>\operatorname{graph}\,L\subset X\times Y</math> then the inverse relation is <math>L^{-1} : Y \to X</math> defined by <math>y\,L^{-1}\,x\iff x\,L\,y</math>, i.e. with <math>\operatorname{graph}\,L^{-1} = \{(y, x)\in Y\times X\mid (x, y) \in \operatorname{graph}\, L\}</math>. The notation comes by analogy with that for an inverse function. The inverse relation is also called the converse relation or transpose relation, and may be written as <math>L^C</math>, <math>L^T</math>, or <math>\breve{L}</math>. Note that, despite the notation, the converse relation is not an inverse in the sense of composition of relations: <math>L \circ L^{-1} \neq \mathrm{id}</math> in general.
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  • In mathematics, the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'.
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  • Inverse relation
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