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  text: 'A binary [-3nt] $R$ is **transitive** if whenever $aRb$ and $bRc$, $aRc$. \n\nThe most common examples or transitive relations are [3rb partial orders] (if $a \\leq b$ and $b \\leq c$, then $a \\leq c$) and [53y equivalence relations] (if $a \\sim b$ and $b \\sim c$, then $a \\sim c$).\n\nA transitive relation that is also [5dy reflexive] is called a [-preorder].\n\nA [-transitive_set] $S$ is a set on which the element-of relation $\\in$ is transitive; whenever $a \\in x$ and $x \\in S$, $a \\in S$.',
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