= Solution
Every finite <formal language> is a <regular language>. A single <string> $a_1\cdots a_k$ is described by the <regular expression> formed by concatenating its symbols; the empty <string> is described by $\varepsilon$. A finite <union> of these <regular expressions> describes any specified finite collection of <strings>. The empty collection is described by $\varnothing$. Thus
$$
\boxed{\text{every finite subset of }\{0,1\}^*\text{ is regular}.}
$$
Equivalently, a <deterministic finite automaton> can remember which <prefix> of one of the finitely many accepted <strings> has been read, moving to a rejecting dead state when no such <prefix> remains possible.
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