42 lines
1.0 KiB
TeX
42 lines
1.0 KiB
TeX
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In order for this relation to be an equivalence equation, it has to be reflexive, symmetric and transitive.
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\textbf{Reflexive:}
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All elements are related to themself
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\[ AA, DD, CC, EE, BB \]
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\textbf{Symmetric:}
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All relations has its symmetric counterpart
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\begin{gather*}
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AE\text{ and }EA \\
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AC\text{ and }CA \\
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BD\text{ and }DB \\
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CE\text{ and }EC
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\end{gather*}
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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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DB\text{ and }BD\text{ with }DD \\
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AE\text{ and }EA\text{ with }AA \\
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AE\text{ and }EC\text{ with }AC \\
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AC\text{ and }CE\text{ with }AE \\
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AC\text{ and }CA\text{ with }AA \\
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BD\text{ and }DB\text{ with }BB \\
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CE\text{ and }EA\text{ with }CA \\
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CE\text{ and }EC\text{ with }CC \\
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EA\text{ and }AE\text{ with }EE \\
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EA\text{ and }AC\text{ with }EC \\
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EC\text{ and }CE\text{ with }EE \\
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EC\text{ and }CA\text{ with }EA \\
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CA\text{ and }AE\text{ with }CE \\
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CA\text{ and }AC\text{ with }CC
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\end{gather*}
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Hence the relation is an equivalence relation
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