Question

Show that if $f:A\to B$ and $g:B\to C$ are one-one, then $g\circ f:A\to C$ is also one-one.

Answer 1

Given $f:A\to B$ is one one

$a_i\in A,b_i\in B$

$f\left(a_i\right)=b_i$

$g:A\to B$ is one one

$b_i\in B,c_i\in C$

$g\left(b_i\right)=c_i$ for all $b_i$

$g\left(f\right(a_i\left)\right)=c_i$ for all $a_i$ only one $c_i$

$g\left(f\right(x\left)\right)$ is one one.