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