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in Theory of Computation by (139 points) | 57 views
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test series questions should be provided by the source of test series questions @amit166

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The correct answer is C

Obviously the complement of the set of finite languages will be an infinite set hence the given language L is not closed under complementation

by (788 points)
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what about other options ?
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@satbir

Bro every finite language is regular. So L is a set of ALL regular languages and regular languages are closed under union,intersection & complementation right ? Is my thinking correct ?

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https://gateoverflow.in/299897/common-careless-mistakes

@pranay562 see the 4th point.

Your logic is correct so d is correct.

But remember, set of regular languages are not closed under infinite union and infinite intersection.

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yeah thanks bro
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what about other options ?

@satbir @pranay562

$finite \cup finite = finite$

$finite \cap finite = finite$

and when we take the complement of the set of finite languages then it will be an infinite set

https://gateoverflow.in/129942/theory-proof

 

In fact, it is the beauty of the question that it doesn't want to check your knowledge for closure properties

of regular languages but want to check your overall understanding of the concept.

 

But remember, set of regular languages are not closed under infinite union and infinite intersection.

Along with the infinite union and infinite intersection, regular languages are not closed under infinite

set-difference, subset operation and superset operation

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ok so in this question closure property is wrt finiteness ?
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yes
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