Final answer:
If a decomposition of a string w from a language L shows that xyyz is not in L, then the correct conclusion is that L is not regular, as it fails to satisfy the conditions of the Pumping Lemma for regular languages. Therefore, the correct option is b. L is not regular.
Step-by-step explanation:
The question pertains to a concept in formal language theory, specifically regarding the properties of languages and the Pumping Lemma. The Pumping Lemma is a property that is used to prove whether a language is regular or not. If a language L is regular, then there exists a number p (the pumping length) such that every string w in the language with length at least p can be split into three parts, x, y, and z, satisfying certain conditions. One of these conditions is that for any repetition of y, denoted as yi for i ≥ 0, the string xyiz must also be in L.
If we find a decomposition of w into xyz such that duplicating y once to form xyyz results in a string that is not in L, then we can say that the language L does not satisfy the Pumping Lemma for regular languages. Therefore, option (b) L is not regular and is the correct conclusion to draw. It does not, however, allow us to conclude whether L is context-free or not context-free, as the Pumping Lemma for context-free languages has a different set of requirements.