(a) For the language {w | w has length at least 3, and its third symbol is a 1}, we can construct the following DFA:
\[
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto]
\node[state,initial] (q_0) {$q_0$};
\node[state] (q_1) [right=of q_0]
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