- #1

mikemhz

- 6

- 0

[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.