Let $f :A\to B$ and $g : B\to C$ be two functions and $gof : A\to C$ is defined. Then which of the following statement(s) is/are INCORRECT?

If gof is one-one then g must be one-one.  

If f is surjective and g is injective then gof must be surjective

If gof is into then f must be into.

If f is into and g is onto then gof must be onto function.