If we have that f and f o g (that is, f(g) ) are both injective, must then g be injective?
I find that this is false and I show it with an example, where I have
Here I have that f and f o g are injective but g is not, hence g does not have to be injective.
Is this a correct way to show this at all?
I try again, I have that f and f o g are injective, it follows then that g is injective:
I show this with a contradiction, assume that there exists elements s.t. and also assume that f and f o g are injective.
Then we would have , where
This implies that f o g is not injective, which is a contradiction as it was assumed as a premise it was injective, hence g must be injective.
Am I getting closer? :-)