Final answer:
To recognize the language (01 ∪ 001 ∪ 010), we can create an NFA with three states: A, B, and C. To convert this NFA to a DFA, we use the subset construction method.
Step-by-step explanation:
To create an NFA recognizing the language (01 ∪ 001 ∪ 010), we can use three states: A, B, and C. State A is the start state and has transitions on 0 to state B and on 1 to state C. State B has a transition on 1 to state A, and state C has transitions on 0 to state A and 1 to state A. State A is also the only accepting state.
To convert this NFA to an equivalent DFA, we use the subset construction method. Begin with the start state, which is the epsilon closure of the start state of the NFA. From each state, we compute the epsilon closure and transitions on 0 and 1. The reachable portion of the DFA consists of states A, B, C, AB, and ABC, with state A being the start and the only accepting state.