Toc -regular

Question

If L is a regular Language and R is any language such that L+R is regular,then R is

a)Must be regular

b)May or may not be regular

c)Must be non regular language

d)Must be CFL

Answer 1

Take L as  a*b*

a*b*+a^nb^n = a*b*

Where R HERE IS a^nb^n is cfl 

Now take L as £* 

a*b*+£*=£*     

where £* is ( sigma*)

Here R is £* which is regular so 

R MAY MAY OR MAY NOT REGULAR 

b) option ans 

Comments

awesome,thank you, another question though,is it possible to make  union of 2 non regular languages  =    sigma *(because we are missing out all the regular ones as they are closed under union)?

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Yes it is possible .

a^nb^n ∪( a^nb^n )'= €*

Where (a^nb^n)' is complement of a^nb^n!

Answer 2

Option A. Must be Regular. Union of 2 regular language is regular. We cannot assure regularity in case of other options.

Comments

nope this is not the answer given, so a bit confused.