[PDF] a class of language that is closed under

Explanation: A class of languages that is closed under union and complementation has to be closed under intersection. Correct.
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  • What does it mean for a class of languages to be closed?

    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 same “type” as originally operated on i.e., regular.
  • What does it mean to say a class of language is closed under a particular operation?

    We say a set of languages is closed under an operation if the result of applying the operation to any arbitrary language(s) of the set is a language in the set. For example a set of languages is closed under union if the union of any two languages of the set also belongs to the set.
  • Is the class of regular language closed under concatenation?

    Regular languages are closed under concatenation - this is demonstrable by having the accepting state(s) of one language with an epsilon transition to the start state of the next language. If we consider the language L = {a^n n >=0}, this language is regular (it is simply a*).
  • Regular languages are closed under union, concatenation, star, and complementation.
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