Assuming the definition of a deterministic finite-state automaton (DFA) $D=$ $\left(Q, \Sigma, \delta, q_{0}, F\right)$, what is the extended transition function $\hat{\delta}$ for $D$ ? Also assuming the definition of a nondeterministic finite-state automaton (NFA) $N$, what is $\hat{\delta}$ in this case?

Define the languages accepted by $D$ and $N$, respectively, in terms of $\hat{\delta}$.

Given an NFA $N$ as above, describe the subset construction and show that the resulting DFA $\bar{N}$ accepts the same language as $N$. If $N$ has one accept state then how many does $\bar{N}$ have?