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).

Let x=a:

Since a is unique to be and b is unique to c then is also a one to one function. Hence is injective.

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My issue here is the part where I mention that f(a)=b and g(b)=c. Is this a valid claim?