Let f: A→B be a surjection and g:B→C be such that g∘f is an injection. Prove that both f and g are injections
The Attempt at a Solution
Suppose a = a' then g(f(a)) = g(f(a')) since g∘f is 1-1 we have that f(a) = f(a') hence f is 1-1.
Is this correct?