Exercise 3, § 4

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

Theory of Sets, II, 126

Let X, Y, Y', Z be four sets. Show that

(\mathrm{Y}' \times \mathrm{Z}) \circ (\mathrm{X} \times \mathrm{Y}) = \emptyset \quad \text{if} \quad \mathrm{Y} \cap \mathrm{Y}' = \emptyset

and that

(\mathrm{Y}' \times \mathrm{Z}) \circ (\mathrm{X} \times \mathrm{Y}) = \mathrm{X} \times \mathrm{Z} \quad \text{if} \quad \mathrm{Y} \cap \mathrm{Y}' \neq \emptyset.

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