0
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1answer
78 views

Relation $R$: $R\circ R \subseteq R \implies R$ is transitive

Let $R$ be a relation on $X$, a set. If $R\circ R\subseteq R$, then is $R$ transitive?
2
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1answer
116 views

Why is the term “composition” used to mean a certain binary operation on the set of relations on a given set?

I looked for material relating to compositions of equivalence relations, and was surprised to find the claim (here) that the composition of equivalence relations is not necessarily again an ...