Question

The Kleene closure of a language S always produces an infinite language unless S = ɸ or S = {Λ}.

True or False

Answer 1

False. The Kleene closure of a language S always produces an infinite language, except when S is the empty set (ɸ) or the language that only contains the empty string ({Λ}).

Step-by-step explanation:

The statement is False. The Kleene closure of a language S always produces an infinite language, except when S is the empty set (ɸ) or the language that only contains the empty string ({Λ}).

The Kleene closure of a language S, denoted as S*, is the set of all possible concatenations of zero or more strings from S. When S is not empty or does not only contain the empty string, the Kleene closure will contain an infinite number of strings since there are no restrictions on the number of times the strings can be concatenated.

For example, if S is the language of all strings consisting of the letter 'a', the Kleene closure S* will contain all possible combinations of 'a', including 'a', 'aa', 'aaa', and so on.