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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?

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