Let $S$ and $R$ be transitive relations on set $A$. Is $S∘R$ also transitive?
2026-04-02 15:03:32.1775142212
Is composition of two transitive relations transitive? If not, can you give me a counterexample?
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$S=\{(2,3),(4,5)\}$ and $R=\{(1,2),(3,4)\}$ is a counterexample. They're both transitive, but $S\circ R=\{(1,3),(3,5)\}$ is not.