Ace Test Series: Theory Of Computation - Closure Property

Question

please explain:

Comments

@sourav. it is 1* not 1+ so it is not necessary that every string will contain 1 in it.

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@subhanshu : yes you are correct , i missed $o^{n}1^{*}0^{n}$, it will be non deterministic then.

Thanks

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thanks everyone ,i was thinking i was doing some mistake .

Answer 1

All three options are wrong.
if you follow Chomsky hierarchy, you get that all DCFL is also CFL.
And a CFL is also a CSL.

L = L₁ intersection L₂

L = 0ⁿ1*0ⁿ 

So L is CFL as well as CSL ,REL but not RL.
As 0ⁿ1⁺0ⁿ is DCFL
So option is D.