Let $w\_1, \ldots, w\_m$ and $x$ be vectors in $\mathbb{R}^n$, and $\gamma$ be some constant in $\mathbb{R}$.

How can I prove that the set $\{ x \in \mathbb{R}^n: \max\{w\_1^Tx, \ldots, w\_N^Tx\} \geq \gamma\}$ is not convex in general?

(I'm asking for a proof and not for a counterexample.)

Thanks