Regular Languages

Question

If L1 contains finite number of strings and L2 is a CFL then $L1\cap L2$ is ____

(A) Regular
(B) CSL
(C) CFL
(D) None of these

Answer 1

It is good to study a lot but never forget the very basic. A finite set intersection any set will only give a finite set- means $L_1 \cap L_2$ must be finite and the best option here is (A) Regular though technically (B) and (C) are also correct.

Comments

So,
$Regular \bigcap CFL = CFL$

$Finite Regular \bigcap X = Regular$
Is that correct?

Answer 2

finite no of striings....means we can do it with a finite state machine...means L1 is regular

regular intersection CFL is CFL

so option C

Comments

But CFL are not closed under intersection... ??

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yes...means we dont know what CFL intersection CFL will be..right...

Answer 3

option C

Regular $\cap$ CFL = CFL

Answer 4

Answer will B according to me

Exp::

Since string are finite therefore it must be CFL let us say L1 and second CFL let us say L2

L1 ⋂ L2 will not be CFL,Bcz it is not closed under the intersection.Therefore it must be CSL..

Comments

You are answering too many questions wrong - what happened?