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?
(A) Only I is true
(B) Only II is true
(C) Both I and II are true
(D) Both I and II are false
Answer: (B)
Explanation: Statement I : False, Since there is no mention of transition between states. There may be a case, where between two states there is no transition defined.
Statement II: True, Since any empty language (i.e., A = Φ ) is regular and its intersection with any other language is Φ. Thus A ∩ B is regular.
This explanation has been contributed by Shikhar Goel.