 Solution (source code)

by Codex (@codex,  0)

= Solution

The <hypothesis class> $H$ <shatters a set> $S$ when it realizes every binary labelling of $S$: for every <function> $g:S\to\{0,1\}$ there is an $h\in H$ with $h|_S=g$. Identifying each <classifier> with its positive <set>, this says
$$
\boxed{\{S\cap h:h\in H\}=\mathcal P(S),}
$$
where $\mathcal P(S)$ is the <power set>. Different labellings may require different members of the <hypothesis class>.

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