MA0301/exam_template_graphics/graphics/provePoset.tex

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2021-05-17 18:39:28 +02:00
In order for this relation to be a partial order, it has to be reflexive, antisymmetric and transitive.
\textbf{Reflexive:}
All elements are related to themself
\[ AA, BB, CC, DD \]
\textbf{Antisymmetric:}
No relation have a symmetric counterpart \\
(Listing the ones that don't have a symmetric counterpart would just be listing the whole set) \\
\textbf{Transitive:}
All pair of relations where $xRy$ and $yRz$ has its transitive counterpart
\begin{gather*}
AB\text{ and }BD\text{ with }AD \\
AB\text{ and }BC\text{ with }AC \\
BC\text{ and }CD\text{ with }BD \\
AC\text{ and }CD\text{ with }AD
\end{gather*}
Hence the relation is a partial order