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
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.
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