Question

Let $A$ be a finite set, If $f:A\to A$ is onto. Show that $f$ is one-one

Answer 1

A be a finite set

$f:A$$\to$ A is onto that means every element in $Y$ set has a preimage in $X$ set

That also means that every element in

$X$ must have only one image in $Y$ because both $X,Y$ are equal

so the function is one - one