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How can you prove that the complement of a regular language is regular?
The complement of a regular language is regular because regular languages are closed under complementation. This means that if a language is regular, its complement is also regular.
Are decidable languages closed under any operations?
Yes, decidable languages are closed under operations such as union, intersection, concatenation, and complementation. This means that if a language is decidable, performing these operations on it will result in another decidable language.
Are decidable languages closed under concatenation?
Yes, decidable languages are closed under concatenation.
Are decidable languages closed under intersection?
Yes, decidable languages are closed under intersection.
Are recognizable languages closed under concatenation?
Yes, recognizable languages are closed under concatenation.
How can you prove that the complement of a regular language is regular?
The complement of a regular language is regular because regular languages are closed under complementation. This means that if a language is regular, its complement is also regular.
Are decidable languages closed under any operations?
Yes, decidable languages are closed under operations such as union, intersection, concatenation, and complementation. This means that if a language is decidable, performing these operations on it will result in another decidable language.
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Why are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
Are decidable languages closed under concatenation?
Yes, decidable languages are closed under concatenation.
Are decidable languages closed under intersection?
Yes, decidable languages are closed under intersection.
Are recognizable languages closed under concatenation?
Yes, recognizable languages are closed under concatenation.
How can you prove that the reverse of a regular language is regular?
The reverse of a regular language is regular because for every string in the original language, there exists a corresponding string in the reversed language that is also regular. This is because regular languages are closed under the operation of reversal, meaning that if a language is regular, its reverse will also be regular.
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
