regular languages

Question

If L1, L2 be two arbitrary language, Choose incorrect statement(s)

(i) If L1.L2 is regular, then L2.L1 is also regular.
(ii) L1 = L2 iff L1 \ L2 = ∅ and L2 \ L1 = ∅.
(iii) If L ⊆ Σ∗ and L is finite, then Σ∗ \ L is regular.(\=set difference)

(A) Only (i)
(B) (i) and (ii)
(C) (ii) and (iii)
(D) All

Comments

sukannya 

aⁿb^mb* |m<=n

m = 0 and take b*= null then you get a*

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I am really sorry, actually I misread the question so read $a^m b^n$ where m<n but yours is $a^nb^m$

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Can anyone give a counter example for 2nd statement?

Answer 1

1. false

2,3. true

 

1. let L1=a^(2^n).   L2=a*b*.

    L1 L2=aa*b*=regular......... as smallest string in L1 is 1

   L2 L1=a*b*a^(2^n)=csl....non regular

 

2,3 are simply obvious and straightforward..

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