 # R circ S. I have only seen this circle operator with function compositions, so is this "Set Composition"? If so, then how does it work? The question is "Suppose R and S are relations on a set A. If R and S are reflexive relations, then R circ S is reflexive" select true or false. Bernard Boyer 2022-07-15 Answered
$R\circ S$I have only seen this circle operator with function compositions, so is this "Set Composition"? If so, then how does it work?
The question is
"Suppose R and S are relations on a set A. If R and S are reflexiverelations, then $R\circ S$ is reflexive" select true or false.
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Step 1
When R is a relation on sets G and H (that is, a subset of $G×H$), and S is a relation on sets H and J, then $S\circ R$ is a relation on G and J in which g is related to j if and only if there is some $h\in H$ with gRh and hSj.
Step 2
For example, suppose $\left(g,h\right)\in R$ means that woman g is the mother of person h, and $\left(h,j\right)\in S$ means that person h likes to eat food j. Then $S\circ R$ is the relation which holds for woman g and food j if and only if g is the mother of someone who likes to eat food j.
When R and S are functions, this definition coincides with the composition of the two functions.

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