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: Axiom of Extensionality in set theory | Statement: [Basic Law V, relatedTo, Axiom of Extensionality in set theory]

Target entity: Axiom of Extensionality in set theory
Context triple: [Basic Law V, relatedTo, Axiom of Extensionality in set theory]

• A. Zermelo–Fraenkel set theory
  Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
• B. Zermelo set theory
  Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
• C. axiom schema of separation
  The axiom schema of separation is a principle in set theory that guarantees the existence of subsets defined by properties or predicates, helping to avoid paradoxes by restricting unrestricted set formation.
• D. axiom of choice
  The axiom of choice is a fundamental principle in set theory asserting that one can select an element from each set in any collection of nonempty sets, with far-reaching consequences across mathematics.
• E. Cantor–Bernstein–Schröder theorem
  The Cantor–Bernstein–Schröder theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Axiom of Extensionality in set theory
Triple: [Basic Law V, relatedTo, Axiom of Extensionality in set theory]

The Axiom of Extensionality in set theory states that a set is completely determined by its members, meaning two sets are equal if and only if they have exactly the same elements.

Target entity: Axiom of Extensionality in set theory
Target entity description: The Axiom of Extensionality in set theory states that a set is completely determined by its members, meaning two sets are equal if and only if they have exactly the same elements.

• A. Zermelo–Fraenkel set theory
  Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
• B. Zermelo set theory
  Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
• C. axiom schema of separation
  The axiom schema of separation is a principle in set theory that guarantees the existence of subsets defined by properties or predicates, helping to avoid paradoxes by restricting unrestricted set formation.
• D. axiom of choice
  The axiom of choice is a fundamental principle in set theory asserting that one can select an element from each set in any collection of nonempty sets, with far-reaching consequences across mathematics.
• E. Cantor–Bernstein–Schröder theorem
  The Cantor–Bernstein–Schröder theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above. chosen