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How to prove or disprove that if $R^2$ is reflexive then also $R$ is reflexive ?

I tried to prove $R^2 \supseteq (x,x)\forall x \in R\implies R_{rex}$ but without success, maybe I have to find counetrexample?

lllook
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1 Answers1

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Let $R$ be the relation in $\mathbb{R} \times \mathbb{R}$ defined by $R=\{(x,y) : \vert x-y \vert =1\}$. It is easy to see that $R^2$ is reflexive and $R$ is not.

Ramiro
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