I did it like this:Suppose that f:A B and g:B C are mappings. Show that:
1. f and g are both injective g f is injective
Let , and .
If f and g are injective x,y A, f(x)=f(y) x=y.
Therefore: f(a)=b and g(b)=c where a is unique to b and b is unique to c (one to one function by the injective property).
Since a is unique to be and b is unique to c then is also a one to one function. Hence is injective.
My issue here is the part where I mention that f(a)=b and g(b)=c. Is this a valid claim?