Regular expression-ME

Question

I feel answer is C but it is given "A". anyone help?

Answer 1

I eliminated all the other 3 options,by counter example. Hence option a is the correct answer.

Comments

But according  to option A  string "baba" must be a part of language but it is not part of L1 U L2 compliment??

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Forgot to write it,but L2$\overline{L2}$ will include $\overline{L2} \sum * - L,so that'll be included too.

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Oh i got it now thak you!

Answer 2

Actually the answer given is wrong.

Neither of them is correct.

(a+b)* also contains those string which have a after b or have a substring of abab and many more permutations.

The correct ans would be {aⁿb^m | m,n>=0} 

Proof:

L1: aⁿb^m | n,m >=0 

L2 : aⁿb^m| m=n

L2' : aⁿb^m | m!=n

 Now L2' is a subset of L1 as L1 will contain all the string of form a^nb^n, 

SetA  (union) subset of SetA = SetA

Therefore L will be L1 only.