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Can someone please tell me the difference between them ? not reflexive or irreflexive thank you

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    This closure is ridiculous. There is absolutely nothing to be added to the question. – 2017-01-10
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    Isn't this a reasonable question? A relation R on set S can be neither reflexive nor irreflexive. So a Not reflexive relation can be: 1. Not reflexive and not irreflexive, or 2. irreflexive . Check Wikipedia https://www.wikiwand.com/en/Reflexive_relation – 2018-12-14

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Is this a trick question? None: in both cases, there's no such thing. :) You mean "reflexive" and "irreflexive".

A relation $R \subseteq A \times A $ is reflexive on $A$ if $aRa$ for every $a\in A$. Thus $R$ is not reflexive on $A$ iff for some $a\in A, \text{not } aRa$.

A stronger condition than "not reflexive" is irreflexive. $R$ is irreflexive on $A$ iff for all $a\in A, \text{not } aRa$.

If $A\neq \emptyset$, then "$R \text{ is irreflexive on } A$" implies "$R \text{ is not reflexive on } A$", but the converse is not in general true unless $A$ is a singleton.

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    Maybe it is a "tricky question" ... consider the order of quantifiers : *irreflexive* : $\forall x \lnot (xRx)$; **not** *reflexive* : $\lnot \forall x (xRx)$. – 2017-01-10
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    @MauroALLEGRANZA TrickY, yes, it is that. – 2017-01-10
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On set $A=${$1,2,3$}, consider the relations

$(1)$ $R_1=${$(1,1),(2,2),(3,3),(1,2)$}

$(2)$ $R_2=${$(1,1),(2,2),(1,2)$}

$(3)$ $R_3=${$(1,2),(2,1),(3,1)$}

$R_1$ is reflexive,$R_3$ is irreflexive and $R_2$ is non-reflexive. Can you see the difference?

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    thank you very much for your help – 2017-01-16
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    @Omar Said..accept my answer if you understand it and feel free to ask what else can I do to help you more. – 2017-01-16