## Binary Relations and Their Properties

**Binary relations**, i.e. those relations $R\subseteq S\times T$ defined on elements of some two (not necessarily different) sets $S$ and $T$, are considered particularly important in mathematics. They can be interpreted as assignments of the elements $s\in S$ to the elements $t\in T$. We write such assignments as ordered pairs $(s,t)\in R$ or also as $ s R t $.

| | | | Contributors: *bookofproofs* | References: [573]

## 1.**Definition**: Inverse Relation

## 2.**Explanation**: Representations of Binary Relations

## 3.**Definition**: Total and Unique Binary Relations

## 4.**Definition**: Composition of Binary Relations

## 5.**Definition**: Reflexive, Symmetric and Transitive Binary Relations

## 6.**Definition**: Irreflexive, Asymmetric and Antisymmetric Binary Relations

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[573] **Schmidt Gunther, StrÃ¶hlein Thomas**: “Relationen und Graphen”, Springer-Verlag, 1989

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