![](gateoverflow.com)
![](https://gateoverflow.in/?qa=blob&qa_blobid=5884300907043596528)
![](data:image/png;base64,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)
This should be the DFA for the given language. Since not mentioned explicitly, have taken $\epsilon$ as a member too.
We can frame the equation by looking at the Automata
$\epsilon$ + (0 + 1)0$^*$ + (0 + 1)10$^*$
or you can simplify it to
$\epsilon$ + 00$^*$ + 10$^*$ + 010$^*$ + 110$^*$
$\epsilon$ + 0(0$^*$ + 10$^*$) + 1($\epsilon$ + 1)0$^*$