Final answer:
The statement that regular languages are closed under union is true. If L1 and L2 are regular languages, then their union L1 ∪ L2 is also a regular language, which is a consequence of the closure property of regular languages.
Step-by-step explanation:
Are Regular Languages Closed Under Union?
The statement 'regular languages are regular under reunion' refers to the concept of whether the union (often termed as reunion in this context) of two regular languages is also a regular language. This is true. The closure property of regular languages under union states that if L1 and L2 are two regular languages, then their union L1 ∪ L2 (where ∪ represents the union operation) is also a regular language.
To provide an example, suppose L1 represents the language generated by all strings over the alphabet {a, b} that start with an 'a', and L2 represents the language generated by all strings that end with a 'b'. Both L1 and L2 are regular languages. The union of these two languages would include all strings that either start with an 'a' or end with a 'b', and this union will also be a regular language.
The process of proving this involves constructing a non-deterministic finite automaton (NFA) that recognizes the union of the languages by combining the NFAs of L1 and L2. Since NFAs are equivalent to regular languages, the result is also a regular language, thus confirming the closure property