Study Notes on Closure properties of Languages

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Closure properties on regular languages are defined as certain operations on regular language which are guaranteed to produce regular language. Closure refers to some operation on a language, resulting in a new language that is of the same “type” as originally operated on i.e., regular.

The table below shows the closure properties of all the formal languages. 


Note :Union , Intersection or difference with regular doesn’t change the language. i.e.

Let (AnyLANG) below represents any of the language among DCFl , CFl , CSL , RE or REC

Regular ∩ AnyLANG = AnyLANG

Regular ∪ AnyLANG = AnyLANG

Regular – AnyLANG = AnyLANG 

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