Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: extremal set theory | Statement: [Erdős–Ko–Rado theorem, topic, extremal set theory]

Target entity: extremal set theory
Context triple: [Erdős–Ko–Rado theorem, topic, extremal set theory]

• A. extremal combinatorics chosen
  Extremal combinatorics is a branch of combinatorics that studies how large or how structured a discrete object (such as a graph or set system) can be under given constraints, often focusing on optimal bounds and extremal configurations.
• B. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• C. Ramsey theory
  Ramsey theory is a branch of combinatorics that studies the conditions under which order or structure must appear within sufficiently large or complex mathematical objects.
• D. Sperner family
  A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
• E. Erdős–Stone theorem
  The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.