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  "body": "\n## Definition\n\nLet $A$, $B$ and $C$ be sets, let $R \\subseteq A \\times B$ and let $S \\subseteq B \\times C$ be [[binary relations|08EJC6Q25H]].\nThe composition of $R$ and $S$ is the relation from $A$ to $C$\n$$R \\mathbin{;} S = \\{(a, c) \\in A \\times C \\mid \\exists b \\in B, \\, a \\mathrel{R} b \\text{ and } b \\mathrel{S} c\\}.$$\n\n## Remarks\n\nMany authors write $S \\circ R$ for $R \\mathbin{;} S$. This order agrees with [[function composition|07HF9YCWPP]].\nComposition of relations is associative.\nA relation $R$ on a set is [[transitive|0CYRECG2YQ]] exactly when $R \\mathbin{;} R \\subseteq R$.\n\n## Explanations\n\n### L1 human\n\nLet $R$ be \"is a parent of\" and let $S$ be \"is a parent of\" again.\nThen $R \\mathbin{;} S$ is \"is a grandparent of\": you go from a person to a child, then from the child to a grandchild.\n",
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