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> > Regular languages are closed not only under concatenation and Kleene star, but also: > > - union > Union doesn't belong in the bottom list. Disjunction is

• thaumasiotes 6y ago
  The parent comment says "closed not only under concatenation and Kleene star, but also under these other four operations". That divides the closure properties into two sets, obvious and nonobvious. The obvious ones are obvious because they are regular operations -- concatenation and Kleene star are operators defined by the language of regular expressions. Intersection isn't. I'm pointing out that set union belongs in the obvious group and not the nonobvious group. Like concatenation and Kleene star, it is one of the operators used to define what a regular expression is. To show that regular languages are closed under intersection / complementation / string reversal, you need to do a proof. The proof of closure under set union is just that it's part of the definition of regular expressions.