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: Lubell–Yamamoto–Meshalkin inequality | Statement: [Sperner family, relatedInequality, Lubell–Yamamoto–Meshalkin inequality]

Target entity: Lubell–Yamamoto–Meshalkin inequality
Context triple: [Sperner family, relatedInequality, Lubell–Yamamoto–Meshalkin inequality]

• A. Bogoliubov inequality
  The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
• B. Young's inequality
  Young's inequality is a fundamental result in mathematical analysis that provides an upper bound for the product of two nonnegative numbers in terms of their powers, playing a key role in convex analysis and functional inequalities.
• C. Minkowski inequality
  The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
• D. Hardy–Littlewood–Pólya inequality
  The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
• E. Meyer inequalities
  Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Lubell–Yamamoto–Meshalkin inequality
Target entity description: The Lubell–Yamamoto–Meshalkin inequality is a fundamental result in extremal set theory that bounds the size of a family of subsets of an n-element set by relating it to the structure of maximal chains in the Boolean lattice.

• A. Bogoliubov inequality
  The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
• B. Young's inequality
  Young's inequality is a fundamental result in mathematical analysis that provides an upper bound for the product of two nonnegative numbers in terms of their powers, playing a key role in convex analysis and functional inequalities.
• C. Minkowski inequality
  The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
• D. Hardy–Littlewood–Pólya inequality
  The Hardy–Littlewood–Pólya inequality is a fundamental result in majorization theory and inequalities that characterizes how convex functions behave under rearrangements of sequences or vectors.
• E. Meyer inequalities
  Meyer inequalities are fundamental estimates in Malliavin calculus that relate Sobolev-type norms of random variables to norms involving iterated Malliavin derivatives, playing a key role in regularity and integrability results on Wiener space.
• F. None of above. chosen

Target predicate: relatedInequality
Context triple: [Sperner family, relatedInequality, Lubell–Yamamoto–Meshalkin inequality]

• A. inequality
  Indicates that there is a difference or lack of equality in status, rights, opportunities, or treatment between entities.
• B. relatedPass
  Indicates that one pass is associated with or connected to another pass in some relevant way.
• C. relatedRule
  Indicates that one rule is connected or associated with another rule, typically through some logical, structural, or referential relationship.
• D. relatedByFormula
  Indicates that one entity is mathematically or logically derived from, or connected to, another according to a specific formula.
• E. relatedTheorem
  Indicates that one theorem is connected to another through a logical, thematic, or derivational relationship.
• F. None of above. chosen