#convex-sets

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Which of these subsets of $\mathbb{R}^2$ are convex? Select all that apply.

$\{\mathbf{x} : |x_1| + |x_2| \le 1\}$ 1
$\{\mathbf{x} : \max(|x_1|, |x_2|) \le 1\}$ 2
$\{\mathbf{x} : (\sqrt{|x_1|} + \sqrt{|x_2|})^2 \le 1\}$ 3
$\{\mathbf{x} : x_1 + 2x_2 = 3\}$ 4
$\{\mathbf{x} : \lVert \mathbf{x} \rVert_2 \le 1\} \cup \{\mathbf{x} : \lVert \mathbf{x} - (3, 0) \rVert_2 \le 1\}$ 5

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