Question

Show that a one-one function $f:\{1,2,3\}\to \{1,2,3\}$ must be onto.

Answer 1

Since $f$ is one-one.
Hence every element $1,2,3$ has either of image $1,2,3$ $($But different elements of $f$ should not have same images$)$
Here in each case,
Every image has a corresponding element.
Hence, onto function.
$f:\{1,2,3\}\to \{1,2,3\}$ is onto.
Hence, proved.