Show that for any sets [itex]X, Y , Z[/itex], the canonical function: [itex]\varphi : (X × Y) × Z \rightarrow X × (Y × Z)[/itex] [itex](\varphi((x, y), z) = (x,(y, z)))[/itex] is a bijection. Solution. We can do this by showing that [itex]\varphi[/itex] is injective and surjective.. I can do this by showing [itex]\varphi[/itex] has an inverse (isomorphism theorem). But I would like to know how to show that a function involving cartesian products is injective/surjective.