Which one of the following is CORRECT for given Finite automaton?

Consider the following two statements:

I. If all states of an NFA are accepting states then the language accepted by the NFA is 

∑∗.

II. There exists a regular language A 

 such that for all languages B,                          A∩B is regular.

Which one of the following is CORRECT?

  1. Only 
    I is true
  2. Only 
    II is true
  3. Both I
    and 
    II are true
  4. Both 
    I and 
    II are false

plz also tell what sigma* mean????? 

3Comments
Parth Sharma @parthsharmau
24 Jul 2017 04:47 pm

Sigma * is the universal set or all possible strings over sigma 

so i is wrong as we could have a nfa like q0 to q1 an edge with label a represent only two strings null and a...

 

It does not represent sigma *

 

 

ii lets take  language A as null set we can represent null set with a nfa with and we know that the intersection of null set with any set is null  so ii is true .

I hope only ii is true

shivani @shivani1234
24 Jul 2017 05:41 pm
  • only 2nd statement is true, following are the reasons
  • for 1st statement there might be case when two states in nfa are not linked by any transition
  • 2nd statement is true as there exists A=Ø , intersection of any language with Ø is Ø which itself is a regular language.
Parth Sharma @parthsharmau
24 Jul 2017 05:55 pm

Yes shivani that is correct answer .