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I'm asked to draw a DFA of this {$\epsilon$, 0} but have no clue what it means. Can someone help me understand what the automata is supposed to do?

I know that $\epsilon$ is the symbol for empty word.

As an example having to make an automata for this {w| w contains at least two 0s and at most one 1} is pretty understandable but {$\epsilon$, 0} not so much.

To put it simply I do not understand the problem question I'm asked.

**Edit: I forget to specify that we have the alphabet {0,1}

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The problem is to find a DFA, such that the only two words it accepts are '$\epsilon$' - the empty word, and '0'

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