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Question

# Composition of relations $R_2\circ R_1:\{(x,z)|(x,y)\in R_1\text{ and }(y,z)\in R_2\}$

Solution

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$\textbf{Cartesian product}$ of $A$ and $B$: $A\times B=\{(a,b)|a\in A\text{ and }b\in B\}$

A $\textbf{binary relation}$ from $X$ to $Y$ is a subset of the Cartesian product $X\times Y$ and thus a binary relation is a set of ordered pairs $(x,y)$ with $x\in X$ and $y\in Y$.

The $\textbf{composite}$ $S\circ R$ consists of all ordered pairs $(a,c)$ for which there exists an element $b$ such that $(a,b)\in R$ and $(b,c)\in S$

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