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Preorder

Last updated Nov 1, 2022

# Definition

Let $P$ be a Set and let $R$ be a Preorder Relation

on

P

. Then

(P, R)

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Equivalence Relation

Equivalence Relation

... $x, y \in X$ and $xRy$ , then $yRx$ . Remarks As with s, $\pi{1}(R) = \pi{2}(R) = X$ . We often denote $R$ by $\sim$ or $=$ . If $(x, y) \not\in R$ , then we write $x \not\sim y$ or $x \neq y$ .......

11/7/2022
Every Preorder Relation induces an Order Relation

Every Preorder Relation induces an Order Relation

Statement Let $(P, R)$ be a . Then there exists an $\sim$ on $P$ so that $(P/\sim,R/\sim)$ is a . Proof...

11/7/2022
Preorder

Preorder

Definition Let $P$ be a and let $R$ be a on $P$ . Then $(P, R)$ is a ....

11/7/2022

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