Exercise 5, § 4

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

Theory of Sets, II, 126

Let $(\mathrm{G}_\iota)_{\iota \in \mathrm{I}}$ be a family of graphs and let H be a graph. Show that

\left( \bigcup_{\iota \in \mathrm{I}} \mathrm{G}_\iota \right) \circ \mathrm{H} = \bigcup_{\iota \in \mathrm{I}} (\mathrm{G}_\iota \circ \mathrm{H}) \quad \text{and} \quad \mathrm{H} \circ \left( \bigcup_{\iota \in \mathrm{I}} \mathrm{G}_\iota \right) = \bigcup_{\iota \in \mathrm{I}} (\mathrm{H} \circ \mathrm{G}_\iota).

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