Final answer:
The statement is true because r* includes the empty string as part of the language, requiring the start state in the automaton to be a final state to accept it without any transitions.
Step-by-step explanation:
Regarding the statement "For the language defined by r*, the start state must be the final state." it is true. The language r* denotes the Kleene star applied to a regular expression r, meaning it includes the empty string ε (lambda) and any number of repetitions of strings that match r. Since the empty string is part of the language, the start state in the deterministic finite automaton (DFA) or nondeterministic finite automaton (NFA) representing this language must also be an accept state (or final state), as we need to accept the empty string ε, which requires no transitions from the start state.
For example, for any regular expression r, r* would allow for the language { ε, r, rr, rrr, … } to be accepted. Since the empty string is a valid sequence with zero occurrences of the pattern r, the automaton must be able to accept it without any input, which means the start state is also a final state to ensure the empty string is accepted.