vector space of real valued function on a given set 
well, $a$ is true I guess but not sure , $b$ is true as $\max\{f,g\}=\frac{1}{2}(|f-g|-|f+g|\}$
$c$ is also true as  $f\in V\Rightarrow f^2\in V$ so any polynomial expression will also be in $V$, could any one tell me my logic are correct or not? and help me to solve fully correctly?

Relate $fg$ to $(f+g)^2$ and $(f-g)^2$. 
