Chapter: 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 $sRt$.

Explanations: 1

  1. Definition: Inverse Relation
  2. Definition: Total and Unique Binary Relations
  3. Definition: Composition of Binary Relations
  4. Definition: Reflexive, Symmetric and Transitive Binary Relations
  5. Definition: Irreflexive, Asymmetric and Antisymmetric Binary Relations

Chapters: 1

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  1. Schmidt G., Ströhlein T.: "Relationen und Graphen", Springer-Verlag, 1989