Inverse Relation

Topics: Discrete Mathematics - Relation

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(definition)

The inverse relation of a relation, denoted $R^{-1}$, is defined as:

$$R^{-1}=\{(y,x)\mid (x,y)\in R\}$$

Properties §

Bearing in mind the domain and range of a relation, as well as the Cartesian product, the inverse relation has the following properties:

• $R^{-1}\subseteq \text{ran}\times \text{dom}(R)$
• $(A\times B{)}^{-1}=B\times A$
• ${\varnothing }^{-1}=\varnothing$