[SOLVED] COMP4200 Homework 2

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2.

– 𝐴 & 𝐵 are both regular languages, so according to the theorem that regular languages are closed under complement proves that 𝐴̅ & 𝐵̅ are also regular languages.
– Under the theorem that regular languages are closed under intersection and union, we know that equations like 𝐴 ∩ 𝐵 = ̅𝐴̅̅̅∪̅̅̅𝐵̅̅ are regular.
– 𝐴 − 𝐵 can be written as 𝐴 ∩ 𝐵̅
– As said earlier, under the theorem that regular languages are closed under complement 𝐴 & 𝐵̅ are regular.
– Finally since 𝐴 ∩ 𝐵̅ is a regular language, 𝐴 − 𝐵 is also a regular language.