Relation Composition

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math

For a relation $R\subseteq A\times B$ and $S\subseteq B\times C$ we define the [see page 11, composition] of $S$ and $R$ as $S\circ R\subseteq A\times C$ where $S\circ R=\{(a,c):\mathrm{\exists }b\in B((a,b)\in R\wedge (b,c)\in S)\}$.