Exercise 4, § 6

Tag 03J2, permanent. Cite it as [Bourbaki, Tag 03J2].

Theory of Sets, II, 127

Let G be the graph of an equivalence on a set E. Show that if A is a graph such that $\mathrm{A} \subset \mathrm{G}$ and $\mathrm{pr_1A} = \mathrm{E}$ (resp. $\mathrm{pr_2A} = \mathrm{E}$ ), then

\mathrm{G} \circ \mathrm{A} = \mathrm{G} \quad (\text{resp.} \quad \mathrm{A} \circ \mathrm{G} = \mathrm{G});

furthermore, if $B$ is any graph, we have $(G \cap B) \circ A = G \cap (B \circ A)$ (resp. $A \circ (G \cap B) = G \cap (A \circ B)$ ).

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