Question:
If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.
Solution:
Given, f : A → B and g : B → C are one - one.
Then, gof : A → B
Let us take two elements x and y from A, such that
$(g o f)(x)=(g o f)(y)$
$\Rightarrow g(f(x))=g(f(y))$
$\Rightarrow f(x)=f(y)$ (As, $g$ is one-one)
$\Rightarrow x=y$ (As, $f$ is one-one)
Hence, gof is one-one.