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A regular language over an alphabet ∑ is one that cannot be obtained from the basic languages using the operation ans. Kleene* All of the mentioned Union Concatenation

Question

A regular language over an alphabet ∑ is one that cannot be obtained from the basic languages using the operation ans. Kleene*

All of the mentioned

Union

Concatenation

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Solution

The statement is incorrect. A regular language over an alphabet ∑ is one that can be obtained from the basic languages using the operations of Union, Concatenation, and Kleene*. These operations are fundamental in defining regular languages.

Here's a step-by-step explanation:

  1. Basic Languages: These are the simplest form of languages over an alphabet ∑. They consist of all strings of length 1 over ∑, the empty string, and the empty language.

  2. Union: The union of two languages L1 and L2, denoted as L1 ∪ L2, is a language that includes all the strings that are in L1 or L2 or both.

  3. Concatenation: The concatenation of two languages L1 and L2, denoted as L1.L2 or L1L2, is a language that includes all the strings that can be obtained by taking any string from L1 and any string from L2 and concatenating them.

  4. Kleene*: The Kleene star of a language L, denoted as L*, is a language that includes all the strings that can be obtained by concatenating zero or more strings from L.

A regular language is defined as a language that can be obtained by starting with the basic languages and applying the operations of union, concatenation, and Kleene star a finite number of times.

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