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If the two sets of a binary relation are in fact one and the same set, other properties become relevant. The following properties are fundamental to the concept of equivalence relations, which we will learn about later.

Definition: Reflexive, Symmetric and Transitive Binary Relations

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

  1. reflexive, if \(xRx\) for all \(x\in V\)
  2. symmetric, if from \(xRy\) it follows that $yRx$ for all \(x,y\in V\).
  3. transitive, if from $xRy$ and $yRz$ it follows that $xRz$ for all $x,y,z\in V.$

| | | | | created: 2014-04-02 22:07:36 | modified: 2018-12-14 00:05:32 | by: bookofproofs

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