Let L be a finite language. Consider the following invalid proof that L is infin

Question

Let L be a finite language. Consider the following invalid proof that L is infinite: (a) Since L is finite, it is regular. (b) Since L is regular, the pumping lemma applies to L. (c) There is a pumping length, p, associated with L. (d) Let s be a string such that s elementof L and |s| greaterthanorequalto p. (e) By the pumping lemma, s = xyz such that |y| > 0, |xy| lessthanorequalto p, and xy^kz elementof L for all k greaterthanorequalto 0. (f) Since xy^kz elementof L for all k greaterthanorequalto 0, L is infinite. Indicate which step in this proof is invalid, and explain why it is invalid.

Explanation / Answer

The statement (b) is false. Pumping lemma is applied of infinite languages to check their regularity. Finite language are regular irrespective of pumping lemma.

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