Discussion
Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA is \(\Sigma^{*}\).
II. There exists a regular language \(A\) such that for all languages \(B\), \(A \cap B\) is regular.
Which one of the following is CORRECT?
Answer: B
Only II is true.
Statement I is false. An NFA can have every state accepting and still reject strings, because it may have no transition for some symbol: an NFA with one accepting start state and no transitions accepts only \(\varepsilon\). (It would hold for a complete DFA, where every string reaches some state.)
Statement II is true: take \(A = \varnothing\), which is regular. For every language \(B\), \(A \cap B = \varnothing\), which is regular.
So options claiming I is true are wrong, and so is the option calling both false.
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