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Consider the following two statements: I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ*. II. There exists a regular language A such that for all languages B, A ∩ B is regular. Which one of the following is CORRECT?

1. Only I is true
2. Only II is true
3. Both I and II are true
4. Both I and II are false

Correct answer: Only II is true

Solution

Statement I is false because if all states of an NFA are accepting, it only means that the NFA accepts all strings that can be formed from the input alphabet, but it does not guarantee acceptance of all possible strings in Σ*. Statement II is true as the regular language A can be chosen as the empty set, which ensures that the intersection with any language B remains regular.

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