Let f: A ---> B and g: B ---> C, if both f, g are bijective, show (prove) that g o f : A ---> C is bijective.
There are various ways to prove that assertion, which seems very natural.
You want to be injective and surjective, assuming that and have such properties.
Take two distinct elements and in injective Do you see how to the same idea to prove that is injective too.
. (just the definitions of and surjectivity). Given a why is there a such that ?