GATE | GATE-CS-2016 (Set 2) | Question 52

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)

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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