2.
– π΄ & π΅ are both regular languages, so according to the theorem that regular languages are closed under complement proves that π΄Μ
& π΅Μ
are also regular languages.
– Under the theorem that regular languages are closed under intersection and union, we know that equations like π΄ β© π΅ = Μ
π΄Μ
Μ
Μ
βͺΜ
Μ
Μ
π΅Μ
Μ
are regular.
– π΄ β π΅ can be written as π΄ β© π΅Μ
– As said earlier, under the theorem that regular languages are closed under complement π΄ & π΅Μ
are regular.
– Finally since π΄ β© π΅Μ
is a regular language, π΄ β π΅ is also a regular language.
