◀ ▲ ▶Branches / Set-theory / Definition: Irreflexive, Asymmetric and Antisymmetric Binary Relations

The abovementioned reflexive, symmetric and transitive relations and the following three further properties of binary relations are important for the concept of order relations, which we also will be discussing later.

Definition: Irreflexive, Asymmetric and Antisymmetric Binary Relations

Let \(V\) be a set and \(R\subseteq V\times V\) be a relation \(R\) is called:

1. irreflexive, if \((x,x)\not\in R\) for all \(x\in V\),
2. asymmetric, if from $(x,y)\in R$ it follows $(y,x)\not\in R$ for all \(x,y\in V\),
3. asymmetric, if from $(x,y)\in R$ it follows $(y,x)\not\in R$ for all \(x,y\in V\),

Mentioned in:

Chapters: 1
Definitions: 2 3
Explanations: 4 5
Proofs: 6 7 8 9

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