Hi,
Regular languages are closed under pretty much every property. Except infinte intersection with other regular languages.
I'll give you a simple method to get the correct answer for any question related to "closedness" properties. Whenever they ask you if a class of languages is closed under some property or not, you can either try to comeup with a generic method using which if I give you literally any language of that class, you should be able to give a resulant language which is also of the same type.
Nahi Samjhe? I'll explain, Lets say the question asks you "Are Regular languages closed under union"?
Then your answer should be like "I could take the Regular exp of the language L1 and then take the Regular exp of L2 and then write a new regular exp by just unioning (+) those two regular exp, thus the resultant language will always be regular thus I can say they are always closed".
Now coming to the intersection I can write the proof as, L1 intersection L2 = (L1' union L2')' and we have proof of RL being closed under union and complementation (You can complement the DFA for getting the complement of the language), thus we can say that RL are closed under intersection.
TIP: Always try to reason why your answer is correct and why the other given options are not, this will strengthen your grip over the subject.
PS: If your query was resolved please consider upvoting !
