Reflexive and Symmetric Relations

For an arbitrary set AA, let’s define some important types of relations on AA.

Reflexive relation

A relation RR on AA is a reflexive relation if (a,a)R(a,a)\in R for every element that is aAa\in A. If there is an element bAb\in A so that (b,b)∉R(b,b) \not\in R, then RR is not a reflexive relation. Let’s take the set M={α,β,γ}M= \{\alpha, \beta, \gamma\} and consider the following relations:

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