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?

Let us analyze the two statements:

• Statement I is False: In an NFA, transitions on certain alphabet symbols may not be defined for some states. If a string $w$ has no valid path in the NFA, it is rejected even if all existing states are accepting states. For example, an NFA with a single accepting start state and no transitions only accepts $\{\epsilon\}$, not $\Sigma^*$.

• Statement II is True: Consider the regular language $A = \emptyset$ (the empty language). For any language $B$ (whether regular, context-free, or undecidable):

  $$A \cap B = \emptyset \cap B = \emptyset$$

  Since $\emptyset$ is a regular language, there indeed exists a regular language $A$ such that $A \cap B$ is regular for every language $B$.

Hence, only statement II is true.

Therefore, the correct option is (B).