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## Homework Statement

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

## Homework Equations

## 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?